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12) 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.

(Q: 12)
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.

(Q: 12)
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.)
Plot a scatter diagram [Using Excel] and, assuming a linear
relationship, use the least-squares method to find the regression
coefficients b0 & b1.
Interpret the meaning of the Y intercept b0 and the slope b1 in this
problem.
Use the regression equation developed in (a) to predict the assessed
value for a house whose heating area is 1,750 square feet.
Determine the standard error of the estimate.
Determine the coefficient of determination rІ and interpret its meaning
in this problem.
Determine the coefficient of correlation r.
Perform a residual analysis on your results and determine the adequacy
of the fit of the model.
(Continued ( )
At the 0.05 level of significance, is there evidence of a linear
relationship between assessed value and heating area?
Set up a 95% confidence interval estimate of the average assessed value
for houses with a heating area of 1,750 square feet.
Set up a 95% prediction interval of the assessed value of an individual
house with a heating area of 1,750 square feet.
Set up a 95% confidence interval estimate of the population slope.
Suppose that the assessed value for the fourth house was $79,700.
Repeat (a) – (k) and compare the results with your original results.

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