Question

Use the following information for questions 28-31:

Suppose we run a model to determine the test score of a student based in their IQ and time spent studying. The model can be written as:

Score = B₀ + B₁ IQ + B₂ Sleep Hours + B₃ Study Hours + e

Where:

Score = student's score on the test (out of 100)

IQ = student's IQ score (representing intelligence in this model)

SleepHours = number of hours slept the night before the test

StudyHours = number of hours spent studying for the test

Running this regression results in the following output:

	Coefficients	Std. Error	t-stat	P-value
Intercept	23.156	15.967	1.450	0.190
IQ	0.509	0.181	2.818	0.026
SleepHours	0.125	0.087	3.472	0.008
StudyHours	0.467	0.172	2.717	0.030

28.

Which coefficients are significant at the 1% level?

Group of answer choices

IQ, SleepHours, StudyHours

SleepHours and StudyHours

Only SleepHours

Only StudyHours

29.

Which of the following actions would be most likely to lower the R² value for this regression?

Group of answer choices

Removing the variable “Sleep Hours” from the model

Including a variable in the model that has no explanatory power

Including a variable that is negatively correlated with the dependent variable

None of the above

30.

Which of the following statements is true regarding the above regression output?

Group of answer choices

None of the independent variables had a statistically significant effect on the dependent variable.

Students with a higher IQ will always earn a higher score on the test.

All of the independent variables are significant at the 5% level.

On average, an extra hour of sleep will increase a student’s score more than an extra hour of studying, holding all other variables constant.

31.

If the value of adjusted R² increases when adding a new variable, what must also be true?

Group of answer choices

The statistical significance of all independent variables decreases

The value of R2 also increases

The value of R2 decreases

The value of R2 stays the same

Answer 1

Question (28)

If the p-value of the coefficients are less than 0.01 which is the significance level here, then they are significant

Here the p-value of only Sleephours is less than 0.01, Hecne only Sleephours is significant

So Answer is Option C

Question (29)

Since Sleephours is significant variable, removing the Sleephours variable will decrease the value of R-square since no other variables are significant

So Asnwer is Option A

Question (30)

IQ variable's coefficient is positive 0.509 which implies that score of a student has a direct or positive relationship with Student's IQ which implies that as the student IQ increase, the score of the student too increases

So Answer is Option B

Question (31)

When adding a new variable, if the Adjusted R-square increases, then the R-square should also increase. Generally adding new variables to the model will only increase the R-square

So Answer is Option B