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# Application of Regression Analysis

1. Use the graph (see attachment) to describe the total variation about a regression line in words and in symbols.

3. Use the graph (see attachment) to describe the unexplained variation about a regression line in words and in symbols.

11. Retail Space and Sales - The following table (see attachment) represents the total square footage (in billions) of retailing space at shopping centers and their sales (in billions of U.S. dollars) for 11 years. The equation of the regression line is: y = 230.8x - 289.8

13. Earnings of Men and Women - The following table (see attachment) represents median weekly earnings (in U.S. dollars) of full-time male and female workers for five years. The equation of the regression line is: y = 0.898x- 82.291

15. Campaign Money - The money raised and spent (both in millions of U.S. dollars) by all congressional campaigns for eight recent years are shown in the table (see attachment). The data can be modeled by the regression equation:
y = 1.020x - 25.854

16. Fund Assets - The following table (see attachment) represents the total assets (in billions of U.S. dollars) of equity funds and bond and income funds for nine years. The equation of the regression line is y = 0.689x + 68.861

*See attachment for diagram corresponding to 29 and 30
29. Coefficient of Determination - Find the coefficient of determination. What can you conclude?
30. Error of Estimate - Find the standard error of estimate Se and interpret the results.

#### Solution Preview

1. Use the graph to describe the total variation about a regression line in words and in symbols.
The sum of the squares of the differences between the y values of each ordered pair and the mean of y.
Total variations=
3. Use the graph to describe the unexplained variation about a regression line in words and in symbols.
The sum of the squares of the differences between the y-value of each ordered pair and each corresponding predicted y-value.
Unexplained variation=
11. Retail Space and Sales The following table represents the total square footage (in billions) of retailing space at shopping centers and their sales (in billions of U.S. dollars) for 11 years. The equation of the regression line is:
ŷ=230.8x - 289.8

To find out the slope, we need to find out mean of x and y.
mean of x=(1.6+2.3+3.0+3.4+3.9+4.6+4.7+4.8+4.9+5.0+5.1)/11=3.936364
SSx=(1.6-3.936364)^2+(2.3-3.936364)^2+...+(5.1-3.936364)^2=14.48545
Mean of ...

#### Solution Summary

The applications of regression analysis are examined. The graphs to describe the unexplained variations about a regression line in word is determined.

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