Given are five observations for two variables, x and y. z‘ | 2 9 10 12 17 i50 54

Question

Given are five observations for two variables, x and y. z‘ | 2 9 10 12 17 i50 54 46 23 10 The estimated regression equation for these data is y- 65.24-2.86z a. Compute SSE, SST, and SSR. SSE SST SSR b. Compute the coefficient of determination r2 . 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 answerfit C. Compute the sample correlation coefficient. Enter negative value as negative number. % of the variability in y has been explained by the estimated regression equation (to 1 decimal) (to 3 decimals)

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: yi
Independent Variable: xi
yi = 65.244068 - 2.8644068 xi
Sample size: 5
R (correlation coefficient) = -0.81343686
R-sq = 0.66167953
Estimate of error standard deviation: 12.845628

Parameter estimates:

Analysis of variance table for regression model:

Hence,

a) SSE = 495.03

SST = 1463.2

SSR = 968.17

b) r2 = 0.662

appropriate; 66.2%

c) Sample correlation coefficient = -0.813

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 65.244068 13.146907 0 3 4.9626934 0.0157 Slope -2.8644068 1.1825359 0 3 -2.4222577 0.094

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