Check My Work (1 remaining) Given are five observations for two variables, and i
ID: 3050109 • Letter: C
Question
Check My Work (1 remaining) Given are five observations for two variables, and i 14 12 16 19 Vi59 52 45 12 11 The estimated regression equation for these data is y = 64.46-2.762. a. Compute SSE, SST, and SSR SSE SST SSR b. Compute the coefficient of determination r. Comment on the goodness of fit. (to 2 decimals) (to 2 decimals) (to 2 decimals) (to 3 decimals) The least squares line provided an Select your answer-fit; decimal) % of the variability in y has been explained by the estimated regression equation (to 1 c. Compute the sample correlation coefficient. Enter negative value as negative number. (to 3 decimals)Explanation / Answer
The statistical software output for this problem is:
Simple linear regression results:
Dependent Variable: yi
Independent Variable: xi
yi = 64.456998 - 2.7554806 xi
Sample size: 5
R (correlation coefficient) = -0.93348098
R-sq = 0.87138675
Estimate of error standard deviation: 9.4130738
Parameter estimates:
Analysis of variance table for regression model:
Hence,
a) SSE = 265.82
SST = 2066.8
SSR = 1800.98
b) r2 = 0.871
appropriate; 87.1%
c) Sample correlation coefficient = -0.933
Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 64.456998 7.6239303 0 3 8.4545629 0.0035 Slope -2.7554806 0.61118702 0 3 -4.5084083 0.0204