Given are five observations for two variables x and y The es

Given are five observations for two variables, x and y The estimated regression equation for these data is y = 1 + 2.6x. Compute SSE, SST, and SSR using the following equations (to 1 decimal) Compute the coefficient of determination r2 (to 3 decimals). Does this least squares line provide a good fit? Compute the sample correlation coefficient (to 4 decimals).

Solution

Regression equation is y = 1+2.6x

Thus SSE 5.2

         SST 72.8

         SSR 67.6

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r = SSR/SST = 0.928571

r^2 =

Coeff of determination = 0.862245

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Correlation coefficient = 0.928571

As r is nearly 1, the regression equation will be useful as a line of best fit

xi	1	2	3	4	5
yi	4	7	7	11	15	44	8.8
yi cap	3.6	6.2	8.8	11.4	14
(yi-yicap)^2	0.16	0.64	3.24	0.16	1	5.2	SSE
(yi-y bar)^2	23.04	3.24	3.24	4.84	38.44	72.8	SST
(yi^-ybar)^2	27.04	6.76	0	6.76	27.04	67.6	SSR