Question

The National Association of Home Builders ranks the most and least affordable housing markets based on the proportion of homes that a family earning the median income in that market could afford to buy. Data containing the median income($1000s) and the median sale price($1000s) for a sample of 12 housing markets appearing on the list of most affordable markets were subjected to a simple linear regression analysis. The following results were obtained.

**The regression equation is**

price = - 11.8 + 2.18 income

Predictor Coef StDev

Constant -11.80 12.84

income 2.1843 0.2780

S = 6.634 R-Sq =______

**Analysis of Variance**

Source DF SS MS F P

Regression 1 2717.9 2717.9 ----- 0.0001

Residual Error 10 440.1 ------

Total 11 3158.0

a. Using the analysis of variance table, find

MSE =______ F =_____________

b. Interpret **the slope** of the regression
model.

c. **Calculate** the value of the coefficient of
determination and **interpret** it.

d. Using the estimated regression equation, predicted the value of y if x =$20,000

e. Compute 95% confidence interval for the slope

g. At the 0.05 level of significance, is there evidence of a linear relationship between income and price

Answer #1

a)

MSE = SSE/df(error)=440.1/10=44.01

F=MS(regression)/MS(error)=2717.9/44.01=61.76

b)

here slope reresent that for each $1000 increase in income of a faily on average sale price increase by 2184.3

c) estimated regression equation: price = - 11.8 + 2.18* income

predicted value =(-11.8+2.18*20)*1000=31800

e)

fr 10 df and 95% CI ; crtiical t=2.228

hence 95% confidence interval for the slope =2.1843-/+2.228*0.278 =1.565 ; 2.804

g)

as above interval has all values above 0 ; therefore we can cnclude that slope is signifant

we have sufficient evidence at 0.05 level of a linear relationship between income and price

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