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