Question

In: Math

question 23 Given a data with y as a response variable and x1,x2, and x3 as...

question 23

Given a data with y as a response variable and x1,x2, and x3 as explanatory variable, a regression equation relates y to x1 and another relates y to x1,x2, and x3. Calculate the first degree of freedom df1 for testing

H0:β2=β3=0,HA:β2≠0orβ3≠0.

A. 1

B. 2

C. 3

D. 4

question 25

The following table shows the output of a regression model to explain SAT math scores.

	Coefficient	Standard Error	T Stat	p-value
Intercept	650.11	117.42	5.54	0.000
x	-20.96	35.53	-0.59	0.563
Gender	-47.85	22.55	-2.12	0.091

Can we conclude that there is a statistically significant gender difference in math scores at the 5% level ?

A. Yes

B. No

question 26

The following regression output is obtained from estimating

y=β0+β1x+β2d+β3xd+ϵ

where d is a dummy variable.

	Coefficient	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	?	?	?	?	?	?
x	?	?	?	?	1.91	15.51
d	?	?	?	0.04	?	?
xd	?	?	?	?	1.74	2.89

Is there a significant interaction effect between x and d at 5% significance level?

A. Yes

B. No

question 27

Consider the following estimated regression equation

Salary=55.8+3.6∗(Age)−0.7∗(Gender)

where Gender is a dummy variable that takes 0 for a male and 1 for a female.

Compute the predicted salary for a 43 year old woman.

Expert Solution

question 23

Given a data with y as a response variable and x1,x2, and x3 as explanatory variable, a regression equation relates y to x1 and another relates y to x1,x2, and x3. Calculate the first degree of freedom df1 for testing

H0:β2=β3=0,HA:β2≠0orβ3≠0.

B. 2

( we are testing 2 regression coefficients,df1=2)

question 25

The following table shows the output of a regression model to explain SAT math scores.

	Coefficient	Standard Error	T Stat	p-value
Intercept	650.11	117.42	5.54	0.000
x	-20.96	35.53	-0.59	0.563
Gender	-47.85	22.55	-2.12	0.091

Can we conclude that there is a statistically significant gender difference in math scores at the 5% level ?

B. No

( calculated t= -2.12, P=0.091 which is > 0.05 level. Ho is not rejected)

question 26

The following regression output is obtained from estimating

y=β0+β1x+β2d+β3xd+ϵ

where d is a dummy variable.

	Coefficient	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	?	?	?	?	?	?
x	?	?	?	?	1.91	15.51
d	?	?	?	0.04	?	?
xd	?	?	?	?	1.74	2.89

Is there a significant interaction effect between x and d at 5% significance level?

A. Yes

( 95% CI =(1.91, 15.51) does not contains 0 value, it is significant)

question 27

Consider the following estimated regression equation

Salary=55.8+3.6∗(Age)−0.7∗(Gender)

where Gender is a dummy variable that takes 0 for a male and 1 for a female.

Compute the predicted salary for a 43 year old woman.

Predicted Salary =55.8+3.6∗(43)−0.7∗(1)

=209.9

milcah answered 12 hours ago

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