Applied Statistics in Business and Economics

Correlation & Regression Analysis

Do heavier cars use more gasoline? If so, can we predict the mileage rating of a car given its weight? Suppose 8 cars were randomly chosen and their weights (in hundreds of pounds) and mileage rating (mpg) are recorded.

Weight (x) MPG (y)
27 30
44 19
32 24
47 13
23 29
40 17
34 21
52 14

A) A) If we want to estimate gas consumption based on the weight of car, which variable is the dependent variable and which is the independent variable?
B) B) Draw a scatter diagram [first enter the data in Excel column A & B. Use MegaStat, correlation/regression, scatterplot; or use Excel, Tools, data analysis, regression function to answer questions c-e].
C) C) What is the value of coefficient of correlation (Use Megastat or Excel, Tools, Data Analysis, Regression function)? Is there a linear relationship between the two variables? If so, how strong is the relationship?
D) D) Determine the coefficient of determination (Use Megastat or Excel, Tools, Data Analysis, Regression function). Interpret the result.
E) Write the simple linear regression equation for the least square regression line that shows the relationship between weight of cars and gas consumption (use Megastat or Excel regression coefficients table).
F) Interpret the meanings of regression coefficients (slope and intercept) in the above equation.
G) Predict the mileage rating for a car that weighs 6,000 pounds?

Part 2. A sociologist claims that the success of students in college (measured by their GPA) is related to their family income. For a sample of 20 students, the coefficient of correlation is 0.40.
Using the alpha 0.01 level of significance, can we conclude that there is a positive association between the two variables – family income and students’ GPA? What is the p-value? Interpret. Test using correlation test of hypothesis formula: [see the model example posted in Suepplementary Reading on Correction & Regression posted in Discusson/course materials forum].

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