Question

Q.30

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

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 ofY

e. None of the above is a correct statement

Answer 1

Using Excel

Result

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	213085729.6	213085729.6	8716.566387	1.93376E-13
Residual	8	195568.5027	24446.06284
Total	9	213281298.1
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	1855.347406	221.6705227	8.369842702	3.14965E-05	1344.174264
X	47.07035136	0.504167352	93.36255345	1.93376E-13	45.90773936

1)

proportion of the variation in Y is explained by the regression = R^2

=

0.999083049

standard error of the estimate =

156.3523675

hence option D) is correct

2)

F = 8716.5663

F > critical value

hence this model is significant

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

is correct