A linear regression model is fitted to the data using the statistical software, R. A summary of that model fit is given below: Coefficients Estimate Std. Error t value Pr( > It|) Intercept 3.42 9.826 0.348 0.73 Homework 0.871 0.1155 7.542 1.37e-08 Residual standard error: 9.493 on 32 degrees of freedom Multiple R-squared: 0.64, Adjusted R-squared: 0.6288 3. Which statement about the coefficient of determination is true? OA. About 80% of variability in quiz grades is explained by the linear association with homework grades. The remaining variation OB. About 62.88% of the variability in homework grades is explained by the linear association with quiz grades. The remaining variation is due to chance. OC. About 64% of the variability in quiz grades is explained by the linear association with homework grades. The remaining variation is due to chance. OD. On average about 80% of quiz grades come from homework. due to chance. 4. Use the information in the software output to write the equation for the regression line for this model: ŷ = 5. Use the information given in the software output to find a 95% confidence interval for the true slope of the linear equation representing the relationship between Homework Grade and Quiz Grade. 6. What are the test statistic and the value for the test of Ho : B1 = 0 versus H, : Bi # 0? Test Statistic: and p value:
A linear regression model is fitted to the data using the statistical software, R. A summary of that model fit is given below: Coefficients Estimate Std. Error t value Pr( > It|) Intercept 3.42 9.826 0.348 0.73 Homework 0.871 0.1155 7.542 1.37e-08 Residual standard error: 9.493 on 32 degrees of freedom Multiple R-squared: 0.64, Adjusted R-squared: 0.6288 3. Which statement about the coefficient of determination is true? OA. About 80% of variability in quiz grades is explained by the linear association with homework grades. The remaining variation OB. About 62.88% of the variability in homework grades is explained by the linear association with quiz grades. The remaining variation is due to chance. OC. About 64% of the variability in quiz grades is explained by the linear association with homework grades. The remaining variation is due to chance. OD. On average about 80% of quiz grades come from homework. due to chance. 4. Use the information in the software output to write the equation for the regression line for this model: ŷ = 5. Use the information given in the software output to find a 95% confidence interval for the true slope of the linear equation representing the relationship between Homework Grade and Quiz Grade. 6. What are the test statistic and the value for the test of Ho : B1 = 0 versus H, : Bi # 0? Test Statistic: and p value:
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 25PFA
Related questions
Question
100%
Transcribed Image Text:Homework and Quizzes - An online statistics professor recently collected grades of 34 students from a homework assignment and a quiz covering
the same material. A scatterplot of this data are given below.
Grades on Homework and Quizzes
50
60
70
80
90
100
110
Homework Grade
001
08
09
Quiz Grade
Transcribed Image Text:A linear regression model is fitted to the data using the statistical software, R. A summary of that model fit is given below:
Coefficients
Estimate
Std. Error
t value
Pr( > [t|)
Intercept
3.42
9.826
0.348
0.73
Homework
0.871
0.1155
7.542
1.37e-08
Residual standard error: 9.493 on 32 degrees of freedom
Multiple R-squared: 0.64, Adjusted R-squared: 0.6288
3. Which statement about the coefficient of determination is true?
O A. About 80% of variability in quiz grades is explained by the linear association with homework grades. The remaining variation is due to chance.
O B. About 62.88% of the variability in homework grades is explained by the linear association with quiz grades. The remaining variation is due to chance.
OC. About 64% of the variability in quiz grades is explained by the linear association with homework grades. The remaining variation is due to chance.
OD. On average about 80% of quiz grades come from homework.
4. Use the information in the software output to write the equation for the regression line for this model:
ŷ =
+
5. Use the information given in the software output to find a 95% confidence interval for the true slope of the linear equation representing the relationship between Homework Grade and Quiz
Grade.
6. What are the test statistic and the p value for the test of H, : B1 = 0 versus H. : B1 # 0?
Test Statistic:
and p value:
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