Question

The data is given as follow.

Excel File: data14-17.xlsx

Xi 2      6          9          13        20

Yi 7      18        9          26        23

The estimated regression equation for these data is y= 7.6+.9x.

Compute SSE, SST, and SSR (to 1 decimal).

SSE
SST
SSR

What percentage of the total sum of squares can be accounted for by the estimated regression equation (to 1 decimal)?

---------%

What is the value of the sample correlation coefficient (to 3 decimals)?

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Answer 1

Using Excel Data Analysis tool for Regression

we get the following

Regression Statistics
Multiple R	0.739795
R Square	0.547297
Adjusted R Square	0.396396
Standard Error	6.514087
Observations	5

ANOVA
	df	SS	MS	F	Significance F
Regression	1	153.9	153.9	3.626866	0.152962
Residual	3	127.3	42.43333
Total	4	281.2

Hence,

SSE = 127.3

SST = 281.2

SSR = 153.9

The R-square value is 0.5473 = 54.7%

Percentage of the total sum of squares that can be accounted for by the estimated regression equation = 54.7%

Multiple R value is 0.7398

Value of the sample correlation coefficient = 0.740                              (Rounded to 3 decimals)