Question

13.76 You want to develop a model to predict the selling price of homes based on assessed value. A sample of 30 recently sold single-family houses in a small city is selected to study the relationship between selling price (in thousands of dollars) and assessed value (in thousands of dollars). The houses in the city were reassessed at full value one year prior to the study. The results are in House 1. (Hint: First, determine which are the independent and dependent variables.) a. Construct a scatter plot and, assuming a linear relation- ship, use the least-squares method to compute the regres- sion coefficients bo and bi. bi, in this problem. selling price for a house whose assessed value is b. Interpret the meaning of the Y intercept, bo, and the slope, c. Use the prediction line developed in (a) to predict the d. Determine the coefficient of determination, r2, and inter- e. Perform a residual analysis on your results and evaluate $170,000 pret its meaning in this problem. the regression assumptions.

Answer 1

(a)

In this example independent saaj able i independent Nani able= assessed value olependentva?i blee price oc homes By using given date ae calcad ate 50meteims sum y price of homes a assessed value 4 3e -sum(y): つの23 g243 rn 74.336 页su mlar ai 74.336 In sum Cay): 208748.2 -', sum CY) 2772 . g sum (2) 172200.7 22.30. 08 sum (2) 스 ave nes methed the regression squares li Co efficents bo and bl enere Bl 그 slope ".SSay SS2 (223-Cg) (27729) до 8748.3-

わ 2. g 17220 a-7- ( 22 3 o. 30 SSz6 42s. 4 7312 ptugging a bcve u a ues tn this formulo 42s. 7312 o Le 2.43-040』14 X 74. g3C bo a 6 2.ogo

140 120 100 ◆ Series1 20 20 40 100 60 汝) 0

(b)

Meaning of the y-intercept when assessed value, that is x = 0.

Then y = y-intercept = b0

Therefore, y = b0

Interpretation of slope b1:

y = b0 +b1x

In this equation that is unit change in of x to unit change in y.

(c)

Regression equation is given as below:

Y = -31.51 + 1.63*X

We are given X = $170000 or $170 thousand dollars.

Y = -31.51 + 1.63*170 = 245.59

Predicted selling price = 245.59 thousand dollars

(d)

The value of the R square or coefficient of determination is given as 0.876042885, this means about 87.60% of the variation in the dependent variable selling price is explained by the independent variable assessed value.

(e)

The residual analysis is given as below:

From this plot it is observed that the given population are from normal distributions.