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# Regression Analysis and Predicting Heating Area Assessment

1. Suppose we want to develop a model that can be used to predict assessed value based on heating area. Based on the following sample of 15 homes;
a. Find the regression coefficients a and b
b. Interpret the meaning of the Y intercept a and slope b.
c. Use the regression model to predict the assessed value of a home with heating area equal to 1,750 square feet.
d. Compute the coefficient of determination r-squared (using Excel). What does this figure meaning?
e. At the .05 level of significance is there a linear relationship between assessed value and heating area?

Assessed Value Heating Area
House (\$000) (Thousands of Sq Feet)
1 84.4 2.00
2 77.4 1.71
3 75.7 1.45
4 85.9 1.76
5 79.1 1.93
6 70.4 1.20
7 75.8 1.55
8 85.9 1.93
9 78.5 1.59
10 79.2 1.50
11 86.7 1.90
12 79.3 1.39
13 74.5 1.54
14 83.8 1.89
15 76.8 1.59

2. Think about a good or service you are familiar with. If you were to use regression analysis to develop a model that can be used to determine the price a customer would be willing to pay for that good or service, what independent variables would you include in the model? How would you collect that data?

#### Solution Preview

1. Suppose we want to develop a model that can be used to predict assessed value based on heating area. Based on the following sample of 15 homes;
a. Find the regression coefficients a and b
a = 51.9165, b = 16.633
b. Interpret the meaning of the Y intercept a and slope b.
For zero heating area, the assessed value of the house is 51.9165. For every thousand square feet increase in the heating area, the assessed value of house increases by \$16,633.

c. Use the regression model to predict the assessed value of a home with heating area equal to 1,750 square feet.
For x= 1.75, y = 51.9165 + 16.633*1.75 = 81.024

d. Compute the coefficient of determination r-squared (using Excel). What does this ...

#### Solution Summary

This solution contains step-by-step calculations to determine the regression equation and the coefficients of the equation. It also predicts values using the regression model and asses the evidence of a linear relationship.

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