Question

A researcher performed a regression analysis to predict achievement in physics using the following predictor variables: student gender (1=male, 0=female), emotional intelligence (ei), intelligence quotient (iq), verbal SAT (vsat), and math SAT (msat). The results are shown below.

Call:

lm(formula = physics ~ Gender + iq + ei + vsat + msat, data = physachv)

Residuals:

     Min       1Q   Median       3Q      Max

-18.8370 -5.3765 -0.6288   5.5483 21.7685

Coefficients:

Estimate Std. Error t value Pr(>|t|)   

(Intercept) -60.106031   9.784708 -6.143 4.69e-09 ***

Gender        7.452708 1.334900 5.583 8.13e-08 ***

iq 0.130124 0.069945 ????? 0.0644 .

ei -0.031818 0.071782 -0.443 0.6581   

vsat -0.093475 0.009694 -9.643 < 2e-16 ***

msat 0.357249 0.018651 19.155 < 2e-16 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 7.87 on 189 degrees of freedom

(5 observations deleted due to missingness)

Multiple R-squared: 0.8048, Adjusted R-squared: 0.7996

F-statistic: 155.8 on 5 and 189 DF, p-value: < 2.2e-16

Analysis of Variance Table

Response: physics

Df Sum Sq Mean Sq F value    Pr(>F)   

Gender 1 8100.8 8100.8 130.782 < 2.2e-16 ***

iq     1 8938.3 8938.3 144.302 < 2.2e-16 ***

ei     1 3466.7 3466.7 55.967 2.699e-12 ***

vsat    1 5030.6 5030.6 81.216 2.228e-16 ***

msat 1 22726.1 22726.1 366.897 < 2.2e-16 ***

Residuals 189 11706.9 61.9  

1. As you know, there are several variable selection methods that can be used to determine which variables to include in a regression model. Based on the regression output that has been provided, what method does it appear that this researcher used?

a. Enter. b. Forward. c. Backward

2. You will notice that the t-value for the test of the null hypothesis for the iq coefficient is missing from the output (?????). What would this value be?

a. There is not enough information to determine. b. 1.860 c. 144.302

3. The regression coefficients for the predictor variables in this model are referred to as what type of coefficient?

a. Direct. b. Partial

4. Based on the results of this regression analysis, would it be reasonable to claim that gender causes physics achievement?

a. No, the coefficient for Gender is not statistically significant making it unreasonable to suggest that Gender is causing physics achievement. b. No, although the coefficient for Gender is statistically significant, it would be unwise to suggest that Gender is the cause of physics achievement. c. Yes, the magnitude of the effect for Gender is very large making it reasonable to suggest that Gender is causing physics achievement.

Answer 1

Call: lm(formula = physics ~ Gender + iq + ei + vsat + msat, data = physachv) Residuals: Min 1Q Median 3Q Max -18.8370 -5.3765 -0.6288 5.5483 21.7685 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -60.106031 9.784708 -6.143 4.69e-09 *** Gender 7.452708 1.334900 5.583 8.13e-08 *** iq 0.130124 0.069945 ????? 0.0644 . ei -0.031818 0.071782 -0.443 0.6581 vsat -0.093475 0.009694 -9.643 < 2e-16 *** msat 0.357249 0.018651 19.155 < 2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 7.87 on 189 degrees of freedom (5 observations deleted due to missingness) Multiple R-squared: 0.8048, Adjusted R-squared: 0.7996 F-statistic: 155.8 on 5 and 189 DF, p-value: < 2.2e-16 Analysis of Variance Table Response: physics Df Sum Sq Mean Sq F value Pr(>F) Gender 1 8100.8 8100.8 130.782 < 2.2e-16 *** iq 1 8938.3 8938.3 144.302 < 2.2e-16 *** ei 1 3466.7 3466.7 55.967 2.699e-12 *** vsat 1 5030.6 5030.6 81.216 2.228e-16 *** msat 1 22726.1 22726.1 366.897 < 2.2e-16 *** Residuals 189 11706.9 61.9 

We just pasted the same output given above in coding area to get proper orientation and clear view.

1)

Based on the regression output that has been provided, which model selection method does it appear that this researcher used?

Answer:-

Based on regression it is clearly seen that researcher has applied Backward Method Of Elimination.Since, He has considered All the regressors available for the model building and further each variable would be evaluated for its significance.

2)

Missing t-value for the test of the null hypothesis for the iq coefficient is

T-value = IQ_coeff / std_error

= 0.130124 / 0.069945 = 1.86038

3)

The regression coefficients for the predictor variables in this model are referred to as what type of coefficient?

-->The regression coefficient which are in the model are the partial coefficients since they are the coefficients calculated by keeping all the variables constant.

Hence,The coefficients are partial.

Interpreted as 1 unit change in say(iq) will make B1 unit change in (physics).i.e partial change in physics is observed using B1.

4)

Based on the results of this regression analysis, would it be reasonable to claim that gender causes physics achievement?

From above analysis it is reasonable to claim that "gender causes physics achievement "

Because, p-value(gender) << 0.05 implies that we reject Ho :: Coeff(Gender) = 0 i.e it is statistically significant.

Also t-value = 5.583 .....which is far away from 0 (zero) implies significance of coefficient.

C. Yes, the magnitude of the effect for Gender is very large making it reasonable to suggest that Gender is causing physics achievement

This is the final answer.