Question

Part A

Run a regression on the following dataset. What proportion of the variation in Y is explained by the regression? Also, what is the standard error of the estimate?

X	Y
262	14,041
319	16,953
361	18,984
381	19,870
405	20,953
439	22,538
472	23,985
508	25,641
547	27,365
592	29,967

a. 99.95%, 24,446.06

b. 99.95%; 0.5042

c. 99.91%; 195,568.50

d. 99.91%; 156.35

e. None of the above

Part B

Which of the following statements is correct?

		a. Based on the F statistic, there is evidence of a linear relationship between X and Y
		b. Because the p-value exceeds the level of significance, there is no evidence of a regression relationship between X and Y
		c. Based on the correlation coefficient, one can conclude that there is evidence of a linear relationship between X and Y
		d. The coefficient for the intercept indicates that X contributes significantly in the prediction of Y
		e. None of the above is a correct statement

Answer 1

Sol:

In excel install analysis tool pak and then

Go to data >data analysis >regression

You will get

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.999541419
R Square	0.999083049
Adjusted R Square	0.99896843
Standard Error	156.3523675
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	2.13E+08	2.13E+08	8716.566	1.93E-13
Residual	8	195568.5	24446.06
Total	9	2.13E+08
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	1855.347406	221.6705	8.369843	3.15E-05	1344.174	2366.521
X	47.07035136	0.504167	93.36255	1.93E-13	45.90774	48.23296

From the above output:

R sq=

0.999083049*100=99.91% Std error=156.35 MARK OPTION D d. 99.91%; 156.35 Part B Which of the following statements is correct? F Significance F 8716.566 1.93376E-13 P<0.05 There exists a linear relationship between x and y

ANSWER:

a. Based on the F statistic, there is evidence of a linear relationship between X and Y