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 (x1x1) is the number of hours spent studying, and the second independent variable (x2x2) is the student's GPA.

Study Hours | GPA | ACT Score |
---|---|---|

00 | 22 | 1616 |

33 | 22 | 2121 |

55 | 33 | 2323 |

55 | 44 | 2323 |

66 | 44 | 2424 |

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Step 2 of 2 :

Determine if a statistically significant linear relationship exists between the independent and dependent variables at the 0.050.05 level of significance. If the relationship is statistically significant, identify the multiple regression equation that best fits the data, rounding the answers to three decimal places. Otherwise, indicate that there is not enough evidence to show that the relationship is statistically significant.

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Answer #1

The statistical software output for this problem is:

**Multiple linear regression results:**

Dependent Variable: ACT Score

Independent Variable(s): Study Hours, GPA

ACT Score = 17.264706 + 1.5294118 Study Hours + -0.55882353
GPA

**Parameter estimates:**

Parameter | Estimate | Std. Err. | Alternative | DF | T-Stat | P-value |
---|---|---|---|---|---|---|

Intercept | 17.264706 | 0.68188371 | ? 0 | 2 | 25.319135 | 0.0016 |

Study Hours | 1.5294118 | 0.14705882 | ? 0 | 2 | 10.4 | 0.0091 |

GPA | -0.55882353 | 0.35109813 | ? 0 | 2 | -1.5916449 | 0.2525 |

**Analysis of variance table for multiple regression
model:**

Source |
DF |
SS |
MS |
F-stat |
P-value |
---|---|---|---|---|---|

Model | 2 | 40.905882 | 20.452941 | 139.08 | 0.0071 |

Error | 2 | 0.29411765 | 0.14705882 | ||

Total | 4 | 41.2 |

**Summary of fit:**

Root MSE: 0.38348249

R-squared: 0.9929

R-squared (adjusted): 0.9857

Hence,

Multiple regression equation:

= 17.265 + (1.529) x1 + (-0.559) x2

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 a student's age
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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...

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 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 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.
ACT Score Study Data
Study Hours GPA ACT Score 1 2 19.91 1 2 19.69 2 2 25.52 2 3 29.67 2
4 29.77
A...

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is the selling price of the house, the first independent variable
(x1x1) is the square footage, the second independent variable
(x2x2) is the number of bedrooms, and the third independent
variable (x3x3) is the age of the house.
Effects on Selling Price of Houses...

The table below gives the number of hours spent unsupervised
each day as well as the overall grade averages for seven randomly
selected middle school students. Using this data, consider the
equation of the regression line, yˆ=b0+b1xy^=b0+b1x, for predicting
the overall grade average for a middle school student based on the
number of hours spent unsupervised each day. Keep in mind, the
correlation coefficient may or may not be statistically significant
for the data given. Remember, in practice, it would...

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 table was generated from the sample data of 1010
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games per night, and their final grades in their math class. The
dependent variable is the final grade, the first independent
variable (x1x1) is the number of hours unsupervised each night, and
the second independent variable (x2x2) is the number of hours of
video games each night....

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