MODULE 01 - INTRODUCTION TO SIMPLE AND MULTIPLE LINEAR REGRESSION

Advanced Quantitative Research in the Designed and Built Environment

Simple Linear and Multiple Linear Regression PRESENTED BY |

BRYLL EDISON C. PAR

A. INTRODUCTION TO SIMPLE LINEAR REGRESSION B. HOW TO PERFORM LINEAR REGRESSION C. MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

PART 1 – Introduction to Simple Linear Regression PRESENTED BY |

BRYLL EDISON C. PAR

UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

Advanced Quantitative Research in the Designed and Built Environment

Regression models describe the relationship between variables by fitting a line to the observed data.

Linear regression models use a straight line, while logistic and nonlinear regression models use a curved line. Regression allows you to estimate how a dependent variable changes as the independent variable(s) change.

FIGURE 1 – LINEAR REGRESSION MODEL

FIGURE 2 – LOGISTIC AND NONLINEAR REGRESSION MODEL

SOURCE: https://www.scribbr.com/statistics/simple-linear-regression/ IMAGE REFERENCES: From left-analyticsvidhya.com; Nwaogazie (2017) INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

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Linear regression attempts to model the relationship between two variables by fitting a linear equation to observed data. One variable is considered to be an explanatory variable, and the other is considered to be a dependent variable.

SOURCE: stat.yale.edu IMAGE REFERENCES: From left-Scribbr; Auerkari, e at.,(2017); sphweb.bumc.bu.edu INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

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Objectives of Linear Regression To establish if there is a relationship between two variables:

Forecast new observations: -

-

More specifically, establish if there is a statistically significant relationship between the two.

Examples: Income and spending, wage and gender, and student height and exam scores.

-

Can we use what we know about the relationship to forecast unobserved values?

Examples: What will our sales be for the next quarter?

What will the ROI of a new store opening be contingent on store attributes.

Variable Roles

The Magic

• •

Slope-intercept form • y = a+bx • y = mx+b

Dependent Variable – Denoted by “y” Independent Variable – Denoted by “x”

Linear Equation in Statistics y = β0 + β1x where: β0 = Intercept/constant value β1 = slope of x SOURCE: Introduction to Simple Linear Regression by dataminingincae found at YouTube.com INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

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Note: We call it “linear equation” because the equation represents a straight line in a bi-dimensional plot

Change in intercept

Change in slope Slope-intercept form • y = a+bx • y = mx+b

SOURCE: Introduction to Simple Linear Regression by dataminingincae found at YouTube.com INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

Advanced Quantitative Research in the Designed and Built Environment

Simple Linear Regression

Error Term

Linear Regression Model

Linear Regression Equation

y = β0 + β1x + ε

y = β0 + β1x

where: y = Dependent Variable x = Independent Variable β0 = Intercept/constant value β1 = Coefficient/slope of x

where: y = Dependent Variable x = Independent Variable β0 = Intercept/constant value β1 = Coefficient/slope of x Note: There is no error term since the error is assumed to be zero

ε = error term SOURCE: Introduction to Simple Linear Regression by dataminingincae found at YouTube.com

INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

PART 2 – How to Perform Linear Regression PRESENTED BY |

BRYLL EDISON C. PAR

UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

Advanced Quantitative Research in the Designed and Built Environment

Example: Family’s consumption of a given product (Relationship between the family’s income and the consumption)

Step 1. Compile the observations/true value on a table in the Microsoft Excel program and save it as a CSV. File.

SOURCE: Introduction to Simple Linear Regression by dataminingincae found at YouTube.com INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

Advanced Quantitative Research in the Designed and Built Environment

Example: Family’s consumption of a given product (Relationship between the family’s income and the consumption)

SOURCE: Introduction to Simple Linear Regression by dataminingincae found at YouTube.com INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

Advanced Quantitative Research in the Designed and Built Environment

Example: Family’s consumption of a given product (Relationship between the family’s income and the consumption)

Step 2. Review the linear regression model and identify the independent as well as the dependent variable.

SOURCE: Introduction to Simple Linear Regression by dataminingincae found at YouTube.com INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

Advanced Quantitative Research in the Designed and Built Environment

Example: Family’s consumption of a given product (Relationship between the family’s income and the consumption) Linear Regression Model

Explanation

y = β0 + β1x + ε

CONSUMPTION = β0 +

where: y = Dependent Variable x = Independent Variable β0 = Intercept/constant value β1 = Coefficient/slope of x

where: y = Consumption x = Income β0 = Intercept/constant value β1 = Coefficient/slope of x

ε = error term

β1

ε = error term

Assumption: Income explains consumption

SOURCE: Introduction to Simple Linear Regression by dataminingincae found at YouTube.com INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

INCOME +

ε

Advanced Quantitative Research in the Designed and Built Environment

Example: Family’s consumption of a given product (Relationship between the family’s income and the consumption)

Step 3. Find the coefficients of the constant and the independent variable In this case an open-source statistical package will be used (Gretl software) The software may be downloaded on this link: http://gretl.sourceforge.net/win32/

SOURCE: Introduction to Simple Linear Regression by dataminingincae found at YouTube.com; Gretl Tutorial 1: Simple Linear Regression by dataminingincae Found at YouTube.com INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

Advanced Quantitative Research in the Designed and Built Environment

Example: Family’s consumption of a given product (Relationship between the family’s income and the consumption)

Open Gretl software

Click the file tab and hover to open data and user file

SOURCE: Introduction to Simple Linear Regression by dataminingincae found at YouTube.com; Gretl Tutorial 1: Simple Linear Regression by dataminingincae Found at YouTube.com INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

Advanced Quantitative Research in the Designed and Built Environment

Example: Family’s consumption of a given product (Relationship between the family’s income and the consumption)

A window will pop up. Locate your csv file from your pc and then click open

After you click open, you will be redirected to this window

SOURCE: Introduction to Simple Linear Regression by dataminingincae found at YouTube.com; Gretl Tutorial 1: Simple Linear Regression by dataminingincae Found at YouTube.com INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

Advanced Quantitative Research in the Designed and Built Environment

Example: Family’s consumption of a given product (Relationship between the family’s income and the consumption)

Select both the dependent and independent variable (income and consumption) and then click the Beta icon below

Choose consumption by clicking the blue arrow pointing right

SOURCE: Introduction to Simple Linear Regression by dataminingincae found at YouTube.com; Gretl Tutorial 1: Simple Linear Regression by dataminingincae Found at YouTube.com INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

Advanced Quantitative Research in the Designed and Built Environment

Example: Family’s consumption of a given product (Relationship between the family’s income and the consumption)

Choose income by clicking the green arrow pointing right below the blue arrow then click OK

A window will pop up showing the summary of the data you need

SOURCE: Introduction to Simple Linear Regression by dataminingincae found at YouTube.com; Gretl Tutorial 1: Simple Linear Regression by dataminingincae Found at YouTube.com INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

Advanced Quantitative Research in the Designed and Built Environment

Example: Family’s consumption of a given product (Relationship between the family’s income and the consumption) Gretl is an open-source statistical package, mainly for econometrics.

Econometrics is the science or field of knowledge that analyses data with statistical models to test hypothesis and reach conclusions.

y = 48.77 + 0.85 x + ε Consumption = 48.77 + 0.85 income + ε

SOURCE: Introduction to Simple Linear Regression by dataminingincae found at YouTube.com; Gretl Tutorial 1: Simple Linear Regression by dataminingincae Found at YouTube.com INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

Advanced Quantitative Research in the Designed and Built Environment

Example: Family’s consumption of a given product (Relationship between the family’s income and the consumption)

Step 4. Forecast using gretl. Please follow the instructions

SOURCE: Introduction to Simple Linear Regression by dataminingincae found at YouTube.com; Gretl Tutorial 1: Simple Linear Regression by dataminingincae Found at YouTube.com INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

Advanced Quantitative Research in the Designed and Built Environment

Example: Family’s consumption of a given product (Relationship between the family’s income and the consumption)

Hover on the analysis tab and click forecast and wait for another window to pop up

Check the value of the forecast range and click OK

SOURCE: Introduction to Simple Linear Regression by dataminingincae found at YouTube.com; Gretl Tutorial 1: Simple Linear Regression by dataminingincae Found at YouTube.com INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

Advanced Quantitative Research in the Designed and Built Environment

Example: Family’s consumption of a given product (Relationship between the family’s income and the consumption)

A summary of the predictions, standards error and the intervals will open as well as the “Forecast evaluation statistics using 40 observations” not shown in this figure. The graph will also pop up as shown on the next slide SOURCE: Introduction to Simple Linear Regression by dataminingincae found at YouTube.com; Gretl Tutorial 1: Simple Linear Regression by dataminingincae Found at YouTube.com INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

Advanced Quantitative Research in the Designed and Built Environment

Example: Family’s consumption of a given product (Relationship between the family’s income and the consumption)

SOURCE: Introduction to Simple Linear Regression by dataminingincae found at YouTube.com

Estimated vs. Actual Values

INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

Advanced Quantitative Research in the Designed and Built Environment

Example: Family’s consumption of a given product (Relationship between the family’s income and the consumption)

Step 5. Finalize result and proceed with conclusion

SOURCE: Introduction to Simple Linear Regression by dataminingincae found at YouTube.com; Gretl Tutorial 1: Simple Linear Regression by dataminingincae Found at YouTube.com INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

Advanced Quantitative Research in the Designed and Built Environment

Example: Family’s consumption of a given product (Relationship between the family’s income and the consumption) Estimated model of consumption y = 48.77 + 0.85 x + ε Consumption = 48.77 + 0.85 income + ε 48.77 0.85 x

= Interpreted consumption of a family with 0 income = Marginal effect of one unit increase of income on consumption = It doesn’t have an intuitive interpretation meaning that in most cases we will actually be ignoring it.

Conclusion: Income will grow 0.85 for every unit increase in income. Ex: A family's income is 50 dollars more.

0.85x (0.85)(50 dollars) = 42.5 dollars It means that for every 50 dollars of income a family earns more per week, the consumption will grow on average an expected of 42.5 dollars.

SOURCE: Introduction to Simple Linear Regression by dataminingincae found at YouTube.com INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

PART 3 – Multiple Regression PRESENTED BY |

BRYLL EDISON C. PAR

UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

Advanced Quantitative Research in the Designed and Built Environment

Multiple linear regression is used to estimate the relationship between two or more independent variables and one dependent variable.

SOURCE: https://www.scribbr.com/statistics/multiple-linear-regression/ IMAGE REFERENCES: From left – Jacome (2016); scribbr INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

Advanced Quantitative Research in the Designed and Built Environment

Objectives of Multiple Linear Regression You can use multiple linear regression when you want to know: •

You can use multiple linear regression when you want to know:

• How strong the relationship is between two or more independent variables and one dependent variable (e.g. how rainfall, temperature, and amount of fertilizer added affect crop growth)

The value of the dependent variable at a certain value of the independent variables (e.g. the expected yield of a crop at certain levels of rainfall, temperature, and fertilizer addition).

Variable Roles

The Magic

• •

Slope-intercept form • y = a+bx • y = mx+b

Dependent Variable – Denoted by “y” Independent Variable – Denoted by “x”

Multiple Linear Regression Model y = β0 + β1X1 + β2X2 + … βpXp + ε where: β0 = Intercept/constant value β1 = slope of x SOURCE: Introduction to Simple Linear Regression by dataminingincae found at YouTube.com INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

Advanced Quantitative Research in the Designed and Built Environment

Multiple Regression Key Concept

IV

DV

Simple linear regression

(One to one relationship)

IV

IV DV

IV

Multiple regression

(Many to one relationship)

IV

… or more Note: Adding more independent variables to a multiple regression procedure does not mean the regression will be “better” or offer better predictions; in fact, it can make things worse. This is called “Overfitting” The addition of more independent variables creates more relationships among them. So not only the independent variable, but they are also potentially related to each other. When this happen, it is called “Multicollinearity” SOURCE: Introduction to Simple Linear Regression by dataminingincae found at YouTube.com INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

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Multicollinearity – the independent variables are correlated with each other.

The ideal is for all the independent variables to be correlated with the dependent variable but not with each other.

Multiple regression

(Many to one relationship)

IV

In tis example. 10 relationships should be considered.

4 relationships between IV and DV and another and 6 relationships between IV and IV

IV

Note: The more Independent variable added the relationships become numerous. Some independent variables, or set of independent variables, are better at predicting the dependent variable than others. Some contribute nothing.

IV DV

IV

Check for the relationship between each independent variable and the dependent variable.

Consider all the relationships between each independent variables.

The ideal is for all the independent variables to be correlated with the dependent variable but not with each other.

SOURCE: Introduction to Simple Linear Regression by dataminingincae found at YouTube.com INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

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Facts • • • • •

Multiple regression is an extension of simple linear regression.

Two or more independent variable is used to predict/explain the variance in one dependent variable.

Two problems may arise: 1. Overfitting: is caused by adding too many independent variables; they account for more variance but add nothing to the model 2. Multicollinearity: happens when some/all the independent variables are correlated with eachother.

Multiple Linear Regression Model y = β 0 + β 1 X1 + β 2 X2 + … β p Xp + ε Sum of Linear Parameters

Error Term

•

In multiple regression, each coefficient is interpreted as the estimated change in y corresponding to a one unit change in a variable, when all other variables are held constant.

Multiple Linear Regression Equation y = β 0 + β 1 X1 + β 2 X2 + … β p Xp Error Term is assumed to be zero

Estimated Multiple Linear Regression Equation ŷ = b0 + b1X1 + b2X2 + … bpXp b1, b2,…bp are the estimates of β1, β2,…βp

SOURCE: Introduction to Simple Linear Regression by dataminingincae found at YouTube.com INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

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EXAMPLE 1: ESTIMATED MULTIPLE REGRESSION EQUATION Ŷ = 5.344 + 0.025 X1 + 0.234 X2 – 0.529 X3 (Standard form of a multiple regression equation)

ŷ = b0 + b1X1 + b2X2 + … bpXp (Estimated multiple regression equation)

Estimates of a multiple regression model Variables: X1, X2, and X3 Coefficients: 0.025, 0.234, and -0.529 Intercept: 5.344

EXAMPLE 2: INTERPRETTING COEFFICIENTS

Ŷ = 27 + 9 X1 + 12 X2 (Standard form of a multiple regression equation)

X1 = Capital Investments (1000 usd) X2 = Marketing Expenditures (1000 usd) Ŷ = Predicted Exam Score (1000 usd) Note: In multiple regression, each coefficient is interpreted as the estimated change in y corresponding to a one unit change in a variable, when all other variables are held constant.

In this example, 9000 usd is an estimate of the expected increase in sales y, corresponding to a 1000 usd increase in capital investment (X1) when marketing expenditure (X2) are held constant.

SOURCE: Introduction to Simple Linear Regression by dataminingincae found at YouTube.com INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

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Multiple Regression Pre-work/Data Preparation 1. Generate a list of potential variables; independent(s) and dependent.

2. Collect data on the variables.

3. Check the relationships between each independent variable and the dependent variable using scatterplots and correlations.

4. Check the relationships between independent variables using scatterplots and correlations.

5. (Optional) Conduct simple linear regression for each independent and dependent pair.

6. Use the non-redundant independent variables in the analysis to find the best fitting model.

7. Use the best fitting model to make predictions about the dependent variable.

SOURCE: Introduction to Simple Linear Regression by dataminingincae found at YouTube.com INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

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Sample Problem: Regional Delivery Service RDS Data and Variable Naming To conduct your analysis, you take a random sample of 10 past trips and record four pieces of information for each trip: 10 Total miles traveled, 2) number of deliveries, 3) the daily gas price, and 4) total travel time in hours.

Miles Traveled, (X1)

Number of Deliveries, (X2)

Gas Price, (X3)

Travel Time (Hours), (y)

89

4

3.84

7

66

1

3.19

5.4

78

3

3.78

6.6

111

6

3.89

7.4

44

1

3.57

4.8

77

3

3.57

6.4

80

3

3.03

7

66

2

3.51

5.6

109

5

3.54

7.3

76

3

3.25

6.4

SOURCE: Introduction to Simple Linear Regression by dataminingincae found at YouTube.com INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

Advanced Quantitative Research in the Designed and Built Environment

Sample Problem: Regional Delivery Service (Sketching out relationships) Independent Variables

Dependent Variable

Miles Traveled, (X1)

Gas Price, (X3)

Travel Time, (y)

Number of Deliveries, (X2)

SOURCE: Introduction to Simple Linear Regression by dataminingincae found at YouTube.com

6 Relationships Should be Analyzed

INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

Advanced Quantitative Research in the Designed and Built Environment

Sample Problem: Regional Delivery Service – Dependent Variable vs Independent Variable Scatterplots (Using Gretl application) X3 vs. y X1 vs. y X2 vs. y

R squared = 0.862 P Value (F) = 0.000

R squared = 0.840 P Value (F) = 0.000

SOURCE: Introduction to Simple Linear Regression by dataminingincae found at YouTube.com INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

R squared = 0.071 P Value (F) = 0.455

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Sample Problem: Regional Delivery Service – Multicollinearity Scatterplots (Using Gretl application) X1 vs. y

X2 vs. y

X3 vs. y

R squared = 0.914 P Value (F) = 0.000

R squared = 0.127 P Value (F) = 0.313

R squared = 0.248 P Value (F) = 0.143

SOURCE: Introduction to Simple Linear Regression by dataminingincae found at YouTube.com INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

Advanced Quantitative Research in the Designed and Built Environment

Sample Problem: Regional Delivery Service – Correlation Summary Correlation analysis confirms the conclusion reached by visual examination of the scatterplots Redundant multicollinear variables • Miles Travelled and Number of Deliveries are both highly correlated with each other and therefore are redundant; only one should be used in the multiple regression analysis.

Non-contributing variables • Gas price is not correlated with the dependent variable and should be excluded.

Note: For education purposes, all three relationships will be retained.

SOURCE: Introduction to Simple Linear Regression by dataminingincae found at YouTube.com INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

Advanced Quantitative Research in the Designed and Built Environment

Sample Problem: Regional Delivery Service – Individual Summary Output Travel Time (y) vs. Miles Travelled (X1)

Ŷ = 3.186 + 0.0403 (Miles Travelled) Ŷ = 3.186 + 0.0403 X1 An increase in 1 mile will increase delivery time by 0.0403 hours SOURCE: Introduction to Simple Linear Regression by dataminingincae found at YouTube.com INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

Advanced Quantitative Research in the Designed and Built Environment

Sample Problem: Regional Delivery Service – Individual Summary Output Travel Time (y) vs. Number of Deliveries (X2)

Ŷ = 4.845 + 0.498 (Number of Deliveries) Ŷ = 4.845 + 0.498 X2 An increase in 1 delivery will increase delivery time by 0.498 hours SOURCE: Introduction to Simple Linear Regression by dataminingincae found at YouTube.com INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

Advanced Quantitative Research in the Designed and Built Environment

Sample Problem: Regional Delivery Service – Individual Summary Output Travel Time (y) vs. Gas Price (X3)

Ŷ = 3.536 + 0.811 (Gas Price) Ŷ = 3.536 + 0.811 X3 Gas Price is not a variable that contributes to travel time. No need to explore this value.

SOURCE: Introduction to Simple Linear Regression by dataminingincae found at YouTube.com INTRODUCTION TO SIMPLE LINEAR REGRESSION | HOW TO PERFORM LINEAR REGRESSION | MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB

Advanced Quantitative Research in the Designed and Built Environment

Simple Linear and Multiple Linear Regression PRESENTED BY |

BRYLL EDISON C. PAR

A. INTRODUCTION TO SIMPLE LINEAR REGRESSION B. HOW TO PERFORM LINEAR REGRESSION C. MULTIPLE REGRESSION UNIVERSITY OF THE PHILIPPINES – DILIMAN | INTEGRATED GRADUATE PROGRAM (IGP) | URBAN DESIGN STUDIO LAB