Question

The following data was collected to explore how the average
number of hours a student studies per night and the student's GPA
affect their ACT score. The dependent variable is the ACT score,
the first independent variable (x_{1}) is the number of
hours spent studying, and the second independent variable
(x_{2}) is the student's GPA.

**ACT Score Study Data**

A regression Analysis has been performed to estimate the model
and the output is given.

**Regression Statistics**

df | SS | MS | F | Significance F | |
---|---|---|---|---|---|

Regression | 2 | 90.525 | 31.776 | 59.41 | 0.01297 |

Residual | 2 | 0.055 | 0.344 | ||

Total | 4 | 87.138 |

Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
---|---|---|---|---|---|---|

Intercept | 10.28 | 0.87 | 21.713 | 0.00022 | -2.66 | 22.36 |

Study Hours | 7.2 | 1.06 | 31.573 | 0.00745 | 3.69 | 9.34 |

Student's GPA | 2.45 | 0.305 | 31.038 | 0.00144 |
1.41 |

Step 1 of 4:

What is the intercept of the estimated regression equation?

Step 2 of 4:

What is the standard deviation of the error term?

Step 3 of 4:

What is the predicted value of an ACT Score if the student studies 1.5 hours per night, and has a GPA of 3.5?

Step 4 of 4:

If you were testing with a significance level of 0.05, would you recommend removing "GPA" as an explanatory variable for predicting ACT scores?

Answer #1

The following data was collected to explore how the average
number of hours a student studies per night and the student's GPA
affect their ACT score. The dependent variable is the ACT score,
the first independent variable (x1) is the number of hours spent
studying, and the second independent variable (x2) is the student's
GPA.
Study hours
GPA
ACT score
0
2
17
1
2
19
5
2
28
5
3
29
6
4
31
Find the p-value for the...

The following data was collected to explore how the average
number of hours a student studies per night and the student's GPA
affect their ACT score. The dependent variable is the ACT score,
the first independent variable (x1) is the number of hours spent
studying, and the second independent variable (x2) is the student's
GPA.
Effects on ACT Scores
Study Hours
GPA
ACT Score
1
2
17
2
3
18
3
4
20
5
4
31
5
4
31
Step...

The following data was collected to explore how the average
number of hours a student studies per night and the student's GPA
affect their ACT score. The dependent variable is the ACT score,
the first independent variable (x1) is the number of hours spent
studying, and the second independent variable (x2) is the student's
GPA. Effects on ACT Scores
Study Hours GPA ACT Score
4 3 31
4 3 30
3 3 18
2 2 17
2 2 17
Step...

The following data was collected to explore how the average
number of hours a student studies per night and the student's GPA
affect their ACT score. The dependent variable is the ACT score,
the first independent variable (x1x1) is the number of hours spent
studying, and the second independent variable (x2x2) is the
student's GPA.
Effects on ACT Scores
Study Hours
GPA
ACT Score
00
22
1616
33
22
2121
55
33
2323
55
44
2323
66
44
2424
Copy...

The following data was collected to explore how a student's age
and GPA affect the number of parking tickets they receive in a
given year. The dependent variable is the number of parking
tickets, the first independent variable (x1x1) is the student's
age, and the second independent variable (x2x2) is the student's
GPA.
Effects on Number of Parking Tickets
Age
GPA
Number of Tickets
17
2
1
17
2
2
18
2
4
20
2
5
20
3
5
22...

The following table was generated from the sample data of 10
college students regarding the number of parking tickets the
student receives in a semester, the student's age, and the
student's GPA. The dependent variable is the student's GPA, the
first independent variable (x1) is the number of parking tickets,
and the second independent variable (x2) is the student's age.
Coefficients Standard Error t-Stat p-value Intercept −8.593245
1.831876 −4.690952 0.005381 Number of Parking Tickets −0.023715
0.045205 −0.524623 0.622265 Student's Age...

The following data was collected to explore how a student's age
and GPA affect the number of parking tickets they receive in a
given year. The dependent variable is the number of parking
tickets, the first independent variable (x1x1) is the student's
age, and the second independent variable (x2x2) is the student's
GPA.
Effects on Number of Parking Tickets
Age
GPA
Number of Tickets
23
44
99
23
44
88
22
44
66
20
44
55
19
33
55
19...

Research into the relationship between hours of study and grades
show widely different conclusions. A recent survey of graduates who
wrote the Graduate Management Admissions Test (GMAT) had the
following results.
Hours Studied Average Score
(Midpoint)
64 350
72 450
79 550
106 650
99 750
The Excel output for this regression is as following
SUMMART OUTPUT
____________________________
Regression Statistics
____________________________
Multiple R 0.919958
R Square 0.846322
Adjusted R Square 0.795097
Standard Error 71.57225
Observations 5
Anova
___________________________________________________________________________________________
...

Applications I
Consider the following data representing the total time (in hours)
a student spent on reviewing for the Stat final exam and the actual
score on the final. The sample of 10 students was taken from a
class and the following answers were reported.
time score
0 23
4 30
5 32
7 50
8 45
10 55
12 60
15 70
18 80
20 100
Part 1: Use the formulas provided on the 3rd formula sheet to
compute...

A student stays up all night to study for a test. Whenever he
studies, his scores follow a normal distribution with a nominal
score of 95 % and a standard deviation of 2 % (including occasional
extra credit).
a) Write the exact probability (i.e., in terms of the error
function) that this student will score in the range x ± 1 %.
b) Write the exact probability that, with extra credit, he will
achieve better than a perfect score (>100%).

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