Question 1: A researcher conducted a regression analysis to examine the relationship between the number of hours studied and the test scores obtained by a group of students. The regression equation obtained was: ŷ = 5 + 0.8x, where ŷ represents the predicted test score and x represents the number of hours studied. If a student studies for 10 hours, what is the predicted test score?
Answer 1: To find the predicted test score, substitute the value of x into the regression equation: ŷ = 5 + 0.8(10) = 5 + 8 = 13. Therefore, the predicted test score for a student who studies for 10 hours is 13.
Question 2: A company collected data on the advertising expenditure (in thousands of dollars) and the corresponding sales (in thousands of units) over a period of 8 months. The regression equation obtained was: ŷ = 15 + 2x, where ŷ represents the predicted sales and x represents the advertising expenditure. If the company spends $50,000 on advertising, what is the predicted sales?
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Answer 2: To find the predicted sales, convert the advertising expenditure to thousands of dollars (x = 50) and substitute it into the regression equation: ŷ = 15 + 2(50) = 15 + 100 = 115. Therefore, the predicted sales for a company that spends $50,000 on advertising is 115,000 units.
Question 3: A researcher conducted a multiple regression analysis to predict the monthly electricity consumption of households based on three independent variables: household size (x1), average temperature (x2), and income level (x3). The regression equation obtained was: ŷ = 100 + 20x1 + 5x2 + 10x3. If a household has a size of 4, an average temperature of 25 degrees Celsius, and an income level of $50,000, what is the predicted monthly electricity consumption?
Answer 3: To find the predicted monthly electricity consumption, substitute the values of the independent variables into the regression equation: ŷ = 100 + 20(4) + 5(25) + 10(50) = 100 + 80 + 125 + 500 = 805. Therefore, the predicted monthly electricity consumption for a household with a size of 4, an average temperature of 25 degrees Celsius, and an income level of $50,000 is 805 units.
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Question 4: A company conducted a regression analysis to determine the relationship between advertising expenditure (in dollars) and monthly sales (in units) for a particular product. The regression equation obtained was: ŷ = 500 + 0.5x, where ŷ represents the predicted monthly sales and x represents the advertising expenditure. If the company spends $10,000 on advertising, what is the predicted monthly sales?
Answer: To find the predicted monthly sales, substitute the value of x into the regression equation: ŷ = 500 + 0.5(10,000) = 500 + 5,000 = 5,500. Therefore, the predicted monthly sales for the company when spending $10,000 on advertising is 5,500 units.
Question 5: A researcher collected data on the number of hours studied (x) and the corresponding test scores obtained (y) by a group of students. The regression equation obtained was: ŷ = 30 + 2x. If a student studied for 8 hours, what is the predicted test score?
Answer: To find the predicted test score, substitute the value of x into the regression equation: ŷ = 30 + 2(8) = 30 + 16 = 46. Therefore, the predicted test score for a student who studied for 8 hours is 46.
Question 6: A real estate agent wants to predict the selling price of houses based on their size (in square feet). The agent conducted a regression analysis and obtained the equation: ŷ = 50,000 + 100x, where ŷ represents the predicted selling price and x represents the size of the house. If a house has a size of 1,500 square feet, what is the predicted selling price?
Answer 6: To find the predicted selling price, substitute the value of x into the regression equation: ŷ = 50,000 + 100(1,500) = 50,000 + 150,000 = 200,000.
Therefore, the predicted selling price for a house with a size of 1,500 square feet is $200,000.
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