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