Homework Content

Question 1 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. Predicted equation or equation of the regression line (Y predicted or hat) = 0.725983X + 16.5523

7. Level of Significance = 0.1

8. Critical Value= 0.378419

Question : Based on the linear correlation coefficient (r) in Line 1, the variables(X,Y) are positively correlated

True

False

Question 2 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. Predicted equation or equation of the regression line (Y predicted or hat) = 0.725983X + 16.5523

7. Level of Significance = 0.1

8. Critical Value= 0.378419

Question: Define the Y intercept of the regression line. What is the Y intercept?

A. The Y intercept is the value of Y when the X = 0.

B. It is 16.5523 and is obtained from the regression line: Y hat = .725983 + 16.5523

C. It is .725983 and is obtained from the regression line: Y hat = .725983 + 16.5523

D. Both A and B

Question 3 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 meant by SSR? Which number measures the variation explained by the regression line?

A. Sum of the Squares Regression (SSR); amount of variation in Y explained by the variation in X explanatory variable

B. Sum of the Squares Regression (SSR); amount of variation in X explained by the variation in Y

C. SSR is the percent variation in total variation SST that is explained by the variation in X or SSR/SST = 5182.41/8208.90 = 0.631319 or 63%

D. Both A and C

Question 4 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: How the test whether the Null Hypothesis should be rejected or not?

A. We compare the test statistic of 0.794556 to the critical value of 0.378419 to see if the Null Hypothesis should be rejected. Since t = .795 > critical value(table), reject the null hypothesis of a ZERO relationship.

B. We compare the test statistic of 0.794556 to the critical value of 0.378419 to see if the Null Hypothesis should be rejected. Since t = .795 > critical value(table), do not reject the null hypothesis of a ZERO relationship.

C. None of the above

Question 5 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. Predicted equation or equation of the regression line (Y predicted or hat) = 0.725983X + 16.5523

7. Level of Significance = 0.1

8. Critical Value= 0.378419

Question: Which number is the allowable risk of making a Type I error?

A. The allowable risk of making a Type I error is alpha , the Level of Significance or alpha

B. The chances that there is no relationship between Y and X is about 10%. The lower is this chance of no relationship, the greater is the evidence that there slope is not zero.

C. Both A and B

D. None of the above

Question 6 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. 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(rho) = 0

Alternative Hypothesis is rho(rho) is not equal to 0

B. 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(rho) = 0

C. 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:

Alternative Hypothesis is rho(rho) is not equal to 0

D. None of the above

Question 7 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. Predicted equation or equation of the regression line (Y predicted or hat) = 0.725983X + 16.5523

7. Level of Significance = 0.1

8. Critical Value= 0.378419

Question: What is meant by the slope of the regression line? Which number is the slope of the regression line?

A. The slope of the regression line is the vertical change in Y ( dependent variable) for a unit change in the independent variable , X.

B. 0.72598

C. For every unit increase in X, the Y value will increase by .73 times of X.

D. All of the above

Question 8 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. Total variation (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: Which number measures the distances from the prediction line to the actual values?

A. SEE (Unexplained variation) 3026.49

B. SEE (Unexplained variation) 3026.49/Total Variation(8208.90) = 36.8% unexplained

C. Standard Error of the estimate = 12.9668

All of the above

Question 9 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?

A. The standard error of the estimate is the average scatter points about the regression line. It is about 12.968

B. The standard error of the estimate is the average scatter points on the regression line. It is about 12.968

C. Both A and B

D. None of the above