MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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
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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
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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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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