Data for a sample of houses sold recently in the suburb of a large metropolis are given below:
Area of House (hundreds of square feet) Selling Price (thousands of dollars)
20 250
19 220
27 350
28 390
30 320
15 200
25 360
23 290
18 210
35 410
(a) Do a scatter diagram for the data, insert the trend line and add the equation and R2 value to the diagram.
(b) Find SSxx, SSyy and SSxy.
(c) Determine the correlation coefficient. Comment on the value of the correlation coefficient.
(d) Find the regression equation manually. Compare with the equation obtained when doing the scatter diagram.
(e) Find SST, SSR and SSE.
(f) Find the degrees of freedom associated with the sum of squares in part (e).
(g) Find MSR and MSE.
(h) Summarize your findings as an ANOVA table.
(i) Find the coefficient of determination R2.
(j) Find standard error of the estimate se
(k) Test the hypothesis that Y and X are not related. That is, test H0: 1 = 0 vs. H1: 1 0 by using a t-statistic. Use = 0.05.
(l) Find the predicted value of Y given X = 24. Give an interpretation of the predicted value in the context of the problem.
(m) Find a 95% confidence interval for the mean value of Y given X = 24. Give an interpretation of the confidence interval in the context of the problem.