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 (x1) is the number of hours spent studying, and the second independent variable (x2) is the student's GPA.

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

1 | 2 | 17 |

2 | 3 | 18 |

3 | 4 | 20 |

5 | 4 | 31 |

5 | 4 | 31 |

Step 1 of 2: Find the p-value for the regression equation that fits the given data. Round your answer to four decimal places.

Step 2 of 2: Determine if a statistically significant linear relationship exists between the independent and dependent variables at the 0.01 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.

Answer #1

P-value for the regression equation= 0.0008<0.01 (from ANOVA Table), hence regression of ACT score (y) on the number of hours spent studying (x1) and the student's GPA (x2) is significant.

Since R square 0.9992 i.e. 99.92% of total variation in y is explained by linear regression. Hence the linear regression equation is highly significant and good fit for this data. Moreover adjusted R square 0.9983 which is also high hence all to independent variables have significant effect on y.

Now the fitted reggression equation:

and intercept term and the regression coefficients are all significantly present since their p-value<0.01 (see second portion of ANOVA table).

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 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...

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 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...

The following data was collected to explore how the number of
square feet in a house, the number of bedrooms, and the age of the
house affect the selling price of the house. The dependent variable
is the selling price of the house, the first independent variable
(x1) is the square footage, the second independent variable (x2) is
the number of bedrooms, and the third independent variable (x3) is
the age of the house.
Effects on Selling Price of Houses...

The following data was collected to explore how the number of
square feet in a house, the number of bedrooms, and the age of the
house affect the selling price of the house. The dependent variable
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 ten randomly selected
students spent studying and their corresponding midterm exam
grades. Using this data, consider the equation of the regression
line, yˆ=b0+b1x, for predicting the midterm exam grade that a
student will earn based on the number of hours spent studying. Keep
in mind, the correlation coefficient may or may not be
statistically significant for the data given. Remember, in
practice, it would not be appropriate to use the regression line...

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...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 5 minutes ago

asked 24 minutes ago

asked 35 minutes ago

asked 53 minutes ago

asked 55 minutes ago

asked 55 minutes ago

asked 56 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago