Quantitative Analysis - independent and dependent variables.
Suppose you want to develop a model to predict assessed value based on heating area. A sample of 15 single-family houses is selected in a city. The assessed value (in thousands of dollars) and the heating area of the houses (in thousands of square feet) are recorded with the following results:
House Assessed Value Heating Area of Dwelling
(Thousands of Square 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
(Hint: First determine which are the independent and dependent variables.)
a. Plot a scatter diagram [Using Excel] and, assuming a linear relationship, use the least-squares method to find the regression coefficients b0 & b1.
b. Interpret the meaning of the Y intercept b0 and the slope b1 in this problem.
c. Use the regression equation developed in (a) to predict the assessed value for a house whose heating area is 1,750 square feet.
d. Determine the standard error of the estimate.
e. Determine the coefficient of determination r² and interpret its meaning in this problem.
f. Determine the coefficient of correlation r.
g. Perform a residual analysis on your results and determine the adequacy of the fit of the model. (Continued  )
h. At the 0.05 level of significance, is there evidence of a linear relationship between assessed value and heating area?
i. Set up a 95% confidence interval estimate of the average assessed value for houses with a heating area of 1,750 square feet.
j. Set up a 95% prediction interval of the assessed value of an individual house with a heating area of 1,750 square feet.
k. Set up a 95% confidence interval estimate of the population slope.
l. Suppose that the assessed value for the fourth house was $79,700. Repeat (a) - (k) and compare the results with your original results.