Simple linear regression model
Data for the sample of houses sold recently in suburb of 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 scatter diagram for data, insert trend line and add the equation and R^{2} value to diagram.
(b) Find out SS_{xx}, SS_{yy} and SS_{xy}.
(c) Find out the regression equation manually. Compare with equation obtained when doing scatter diagram.
(d) Now, produce regression report. Compare the equation from regression report with equation obtained manually and while doing scatter plot.
(e) Find out SS_{yy}, SSR, SSE.
(f) Find out the degrees of freedom associated with the sum of squares in part (a).
(g) Find out MSR and MSE.
(h) Summarize your findings as ANOVA table.
(i) Find out the coefficient of determination R^{2}.
(j) Find out standard error of estimate s_{e}
(k) Test the hypothesis that Y and X aren't related. That is, test H_{0}: b_{1 }= 0 vs. H_{1}: b_{1 }¹ 0 by using the t-statistic. Employ a = 0.05.
(l) Find out the predicted value of Y given X = 24. Give the interpretation of predicted value in context of the problem.
(m) Find out 95 % confidence interval for mean value of Y given X = 24. Give interpretation of confidence interval in the context of problem.