Elementary Statistics: A Step By Step Approach
10th Edition
ISBN: 9781259755330
Author: Allan G. Bluman
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 10.3, Problem 1AC
Applying the Concepts 10–3
Interpreting Simple Linear Regression
Answer the questions about the following computer-generated information.
Coefficient of determination = 0.631319
Standard error of estimate = 12.9668
Explained variation = 5182.41
Unexplained variation = 3026.49
Total variation = 8208.90
Equation of regression line y′ = 0.725983x + 16.5523
Level of significance = 0.1
Test statistic = 0.794556
Critical value = 0.378419
1. Are both variables moving in the same direction?
2. Which number measures the distances from the prediction line to the actual values?
3. Which number is the slope of the regression line?
4. Which number is the y intercept of the regression line?
5. Which number can be found in a table?
6. Which number is the allowable risk of making a type I error?
7. Which number measures the variation explained by the regression?
8. Which number measures the scatter of points about the regression line?
9. What is the null hypothesis?
10. Which number is compared to the critical value to see if the null hypothesis should be rejected?
11. Should the null hypothesis be rejected?
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Simple linear regression results:
Dependent Variable: Heart. DiseaseIndependent Variable: BikingHeart. Disease = 18.115809 - 0.20845321 BikingSample size: 68R (correlation coefficient) = -0.94616452R-sq = 0.8952273Estimate of error standard deviation: 1.5273175
Correlation between Biking and Heart. Disease is: -0.94616452.
Correlation between Smoking and Heart. Disease is: 0.32421.
1) State r 2 (i.e., the coefficient of determination) for “Biking” and “Heart.Disease” and explain what this value means in context of the data set.
Interpreting Simple Linear Regression
1. Linear correlation coefficient r = 0.794556
2. Coefficient of Determination ( r square) 0.631319
3. Standard Error of the estimate = 12.9668
4. SSR (Explained variation) = 5182.41
5. SSE ( Unexplained variation) = 3026.49
6. SST = 8208.90
7. Predicted equation or equation of the regression line (Y predicted or hat) = 0.725983X + 16.5523
8. Level of Significance = 0.1
9. Critical Value= 0.378419
10. t test = 0.794556
Question
What is meant by a hypothesis? State the hypothesis in this example?
A hypothesis is a claim about the correlation between the Y and X variables in the population under study:
There are two hypothesis (claims)
Null Hypothesis is that (rho) = 0
Alternative Hypothesis is (rho) is not equal to 0
A hypothesis is a claim about the correlation between the Y and X variables in the population under study:
There is only one hypothesis (claim) as follows:
Null Hypothesis is that (rho) = 0
A…
Interpreting Simple Linear Regression
1. Linear correlation coefficient r = 0.794556
2. Coefficient of Determination ( r square) 0.631319
3. Standard Error of the estimate = 12.9668
4. SSR (Explained variation) = 5182.41
5. SSE ( Unexplained variation) = 3026.49
6. SST = 8208.90
7. Predicted equation or equation of the regression line (Y predicted or hat) = 0.725983X + 16.5523
8. Level of Significance = 0.1
9. Critical Value= 0.378419
Question
What is the meant by the standard error of the estimate? Which number measures the scatter of points about the regression line?
Chapter 10 Solutions
Elementary Statistics: A Step By Step Approach
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