1) Explain briefly what the Standard Errors is and how it can be used an analysi

Question

1) Explain briefly what the Standard Errors is and how it can be used an analysis.

Compare the Standard Errors (SE) of these two models:

Model 1:

Model 2:

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.621798

R Square

0.386633

Adjusted R Square

0.341198

Standard Error

13.8206

Observations

30

ANOVA

df

SS

MS

F

Significance F

Regression

2

3250.843

1625.422

8.509655

0.001362

Residual

27

5157.246

191.0091

Total

29

8408.09

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

-41.4301

12.59216

-3.29015

0.002789

-67.2671

-15.5931

-67.2671

-15.5931

P/E

3.775308

0.978338

3.858901

0.000642

1.767925

5.782692

1.767925

5.782692

Dividend Yield

1.664304

1.766559

0.942116

0.354487

-1.96037

5.288983

-1.96037

5.288983

2) Based on the SE, which model provides a better “fit” for the sample data? Why?

3) Interpret R2 for both the models and briefly explain in plain English.

4) Compare the coefficient of determination (= R2 ) of these two models. Based on R2 , which model provides a better “fit” for the sample data? Why?

5) Briefly explain what the problem in R2 and why Adjusted R2 is more preferable to R2?

6) Compare Adjusted R2 of these two models. Based on Adjusted R2 , which model provides a better “fit” for the sample data? Why?

SUMMARY OUTPUT Regression Statistics Multiple R 0.605367 R Square 0.366469 Adjusted R Square 0.343843 Standard Error 13.79283 Observations 30 ANOVA df SS MS F Significance F Regression 1 3081.307 3081.307 16.19675 0.000393 Residual 28 5326.783 190.2422 Total 29 8408.09 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -38.6971 12.22885 -3.16441 0.003725 -63.7468 -13.6475 -63.7468 -13.6475 P/E 3.89574 0.968001 4.024519 0.000393 1.912879 5.878601 1.912879 5.878601

Explanation / Answer

Part-1: Standard error is the average squared deviation of the points from the regression line. This is used in analysis to know how closely the model is fit. Smaller standard errors are always required as this means points are close to regression line.

Part-2: SE of model 1 is =13.79283

SE of model 2 is =13.8206

As model 1 has lower standard error, so it would be preferred, however the difference is not large.

Part-3: R2 for model 1 is 0.366469 which means that 36.65% of the variations in dependent variable is explained by the predictor P/E.

R2 for model 2 is 0.386633 which means that 38.66% of the variations in dependent variable is explained by the predictor P/E and dividend yield.

Part-4: R2 for model 2 is larger, so model-2 is better fit as it explains more variations in dependent variable.

Part-5: Problem in R2 is that it always increases with increase in the number of predictors. However, adjusted R2 adjust this increase in R2 for sample size and the number of predictors included in the model and adjusted R2 may even decrease if irrelevant predictors are included. That is why, adjusted R2 is preferred.

Part-6: Adjusted R2 for model 1 is 0.343843 and model 2 is 0.341198 and so modle-1 should be preferred. This is because as we saw above that decrease in SE in model 2 and increase in R2 in model 2 are marginal as compared to model 1.

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