Question

Use the table and the given regression equation to answer parts (a)-(e). y = - 1.50 a. Compute the three sums of squares, SST, SSR, and SSE, using the defining formulas. SSTEN (Type an integer or a decimal.) SSR=N (Type an integer or a decimal.) SSEN (Type an integer or a decimal.) b. Verify the regression identity, SST = SSR + SSE. Is this statement correct? O No O Yes c. Determine the value of the coefficient of determination. (Round to four decimal places as needed.) d. Determine the percentage of variation in the observed values of the response variable that is explained by the regression. % (Round to two decimal places as needed.) e. State how useful the regression equation appears to be for making predictions. O A. Very useful O B. Moderately useful O C. Not useful

Answer 1

The statistical software output for this problem is:

Simple linear regression results: Dependent Variable: y Independent Variable: x y = 7.7 - 1.5 x Sample size: 5 R (correlation coefficient)-0.6631285 R-sq 0.43973941 Estimate of error standard deviation: 4.788876 Parameter estimates: Parameter Estimate Std. Err. Alternative DF P-value T-Stat 3.631345 Intercept 7.7 0 3 2.1204264 0.1241 03-1.5344873 0.2225 Slope -1.5 0.97752522 Analysis of variance table for regression model: P-value Source DF SS MS F-stat Model 1 54 54 2.3546512 0.2225 Error 3 68.8 22.933333 Total 4 122.8

Hence,

a) SST = 122.8

SSR = 54

SSE = 68.8

b) Yes

c) r² = 0.4397

d) Percent of variability explained = 43.97 %

e) Moderately Useful