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Regression Lines, Coefficient of Squares, Graphing Dependent and Independent Variables

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Calculating regression lines, coefficient of squares, graphing dependent and independent variables using home sales vs square footage.

1. The data in the table below are the results of a random sample of recent home sales in your neighborhood that your boss has asked you to use to estimate the relationship between the selling price of the house and the number of square feet in it.

Observation Number Sale Price (in thousands) Square Feet (in hundreds)
1 280 20.3
2 328 30.0
3 281 21.5
4 293 25.4
5 263 14.5
6 291 22.3
7 320 31.0
8 256 37.2
9 311 27.1
10 352 30.2
11 288 21.2
12 356 37.2
13 293 23.0
14 272 26.7
15 308 26.5

a. First plot the data, with number of square feet on the "X" axis and the price of the house on the "Y" axis. Explain why housing price is the dependent variable and square feet is the independent variable.
b. What is the estimated regression line? What does the coefficient of square feet represent?
c. Is the sample size large enough for the estimated coefficient of square feet to be statistically significant at the 5% level?
d. What is the coefficient of determination (R2)?
e. Perform an F-test, again at the 5% level.

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Next, run a regression analysis using the BENEFITS column of all data points in the data set as the independent variable and the EXTRINSIC job satisfaction column of all data points in the data set as the dependent variable. Create a graph with the trendline displayed. What is the least squares regression line equation? What are the slope and the y-intercept? What is the R-squared value?
Next, run a regression analysis using the BENEFITS column of all data points in the data set as the independent variable and the OVERALL job satisfaction column of all data points in the data set as the dependent variable. Create a graph with the trendline displayed. What is the least squares regression line equation? What are the slope and the y-intercept? What is the R-squared value?
Finally, make very specific comments and give reasons regarding any similarities or differences in the output results. Which regression produces the strongest correlation coefficient result? Why?

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