Ch. 4Regression Analysis: Exploring Associations between Variables

Answer Key

4.1Visualizing Variability with a Scatterplot

1Compare Scatterplots to Determine Which One Shows a Greater Strength of Association

1)A

6)There are two possible answers here: (1) The number of crimes committed is the explanatory variable and the number of police on patrol is the response because the amount of crime can explain a need for more or less police officers. (2) The number of police on patrol is the explanatory variable and the amount of crime is the response because the more police that are on patrol could explain a reduction in the amount of crime.

7) Scatterplot (ii) shows a stronger linear relationship because it has less vertical variation between points. As a treeʹ s diameter increases, its volume typically increases as well.

2 Describe and Interpret Increasing Trends, Decreasing Trends, or no Trends from Scatterplots

11)Answers may vary. Example: People who spend more time working out tend to lose more weight.

4.2Measuring Strength of Association with Correlation

1Identify and Interpret Correlation in a Scatterplot

18)A correlation coefficient will be negative when there is a negative linear trend in a scatterplot. So, as the values of x increase, the values of y tend to decrease.

19)Scatterplot (i) has the highest correlation because it is more linear than scatterplot (ii). The points have less vertical variation in scatterplot (i), so the relationship is stronger.

20) The correlation coefficient, r, will get closer to 1 because the point is an outlier. Since the rest of the points show a strongly positive linear relationship, r would reflect that and get closer to 1.

2Calculate the Correlation Coefficient of Data

8)The correlation coefficient between the heights of the teenagers in 2003 and 2008 is equal to 1 because for every person, the height increased exactly 6 inches (15.24 cm) from 2003 to 2008. If we plotted the data, the points would form a straight line.

9) a. r = 0.92 b. r = 0.92, The correlation coefficient stays the same. c. r = 0.92. Adding a constant to all y - values does not change the value of r. d. r = 0.92;. The correlation coefficient stays the same.

10)a. r = 0.88 b. r = 0.88. Multiplying by a constant does not change the value of r. c. r = 0.88. Adding a constant does not change the value of r because the strength of the association is not affected.

11) A

12) A 13) A

4.3Modeling Linear Trends

1Predict Values From a Regression Equation

6)Using the regression equation, we find that she has held her current position in the company for approximately 17 year

Salary = 19250 + 3875 (Years in Position)

85,000 = 19,250 + 3875 (Years in Position)

65,750 = 3875 (Years in Position)

16.97 = (Years in Position)

2Interpret or Set Up a Regression Equation and/or Scatterplot

21)The slope is 0.22. For every additional mile of flight travel, the price of the airline ticket is predicted to increase by $0.22.

22)The intercept is 49. If you are traveling 0 miles, the price of an airline ticket is predicted to be $49. The value is not meaningful because you would not pay for an airline ticket if you are not traveling anywhere.

23) b = r s y s x = 0.93 12500 3 = 0.93 4166.67 = 3875.

So, the slope is $3875. For every additional year an employee has held his/her current position in the company, he/she is expected to earn $3875 more for their annual salary.

24)a = y - bx = 58000 - 3875(10) = 58000 - 38750 = 19,250.

So, the intercept is $19,250. If an employee has worked for 0 years in the current position, he/she is predicted to earn a s $19,250. This is reasonable becaue $19,250 could be the employeeʹ s starting salary.

4.4Evaluating the Linear Model

1Apply Concepts for Linear Models

23)No, lower monthly temperatures do not cause gas bills to be more expensive. Correlation never implies causation. We can say that lower temperatures are associated with higher gas bills, but we cannot say that the temperature causes the price.

24) It would not be appropriate to make a prediction because a temperature of - 20° is outside the range of our data. We would be extrapolating.

25)r2 = (- 0.92)2 = 0.8464. This means that 84.64% of the variation in the cost of a gas bill can be explained by the monthly average temperature.

26)r = r2 = 0.379 = 0.6156. Since the plot shows a positive relationship between height and weight, r = 0.6156.

27)The correlation coefficient would be unchanged because it is not affected by changes in units.

28)Answers may vary. Example:

29)The outlier would decrease the slope because it would influence the lower left hand side of the regression line to move closer to it. This would make the line less steep, which results in a smaller slope value.

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