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# HW-1772 Assignment 3 (Score 100%)

Business Stats 2

Due Saturday August 1, 11:59 PM

Assignment 3

NOTE: THERE IS AN EXCEL FILE THAT GOES ALONG WITH THIS ASSIGNMENT. YOU NEED IT TO COMPLETE THE ASSIGNMENT.

Question 1:

Which of the following phrases makes this a correct statement: “If the covariance between two variables is negative, then …

A. … the correlation coefficient will be greater than 1.”

B. … we know for sure that the correlation coefficient between those two variables is also negative.”

C. … the variance of at least one of the variables must be negative”

D. None of the above

Question 2:

Which of the following phrases makes this a correct statement: “If the correlation coefficient between two variables is -1, then …

A. … there is no relationship at all between those two variables.”

B. … all the data points are on a straight line whose slope must be -1.”

C. … all the data points are on a straight line whose slope can be any number (positive or negative).”

D. … all the data points are on a straight line. We do not know what the exact value of the slope is, but we know that the slope is a negative number.”

Question 3:

GENERAL NOTE: Questions 3 through 5 are all based on this first regression.

The “Excel File for Test 3" (also posted under Assignments) contains information about the selling price of houses as well as related information about the houses. Please open the file in Excel and run a regression in which “Selling Price” is your Y input and “Number of Bedrooms” is your X input. Instructions on how to do that are in the Chapter 13 Notes.

Using your regression results, what is the (rounded) value of the estimated intercept “a”?

A. $161,119

B. $15,797

C. $11,716

D. $13.75

Question 4:

What is the value of the estimated slope “b”?

A. $161,119

B. $15,797

C. $11,716

D. $13.75

Question 5:

Is the estimate of the slope statistically significant? (You may want to review the information on scientific notation in the Chapter 13 Notes before answering this question.)

A. Yes, because the p-value is less than 0.05

B. Yes, because the R-Squared is between 0 and 1.

C. No, because the estimate of the slope is smaller than the estimate of the intercept.

D. It is not possible to answer this question because the number of observations is not large enough to make that decision.

Question 6:

GENERAL NOTE: Questions 6 through 8 are all based on this second regression.

Moving to Chapter 14 material (but still using the same Excel file), run one regression with “Selling Price” as the Y input and the following five variables as X variables:

- Number of Baths

- Number of Bedrooms

- Pool (dummy) – 1 indicates “pool”; 0 indicates “no pool”

- Garage (dummy) – 1 indicates “garage”; 0 indicates “no garage”

- Distance to Town Center

Which of the following interpretations of the coefficient on the “Number of Bedrooms” variable is correct?

A. On average, the selling price of a house will increase by approximately $153,678 for an additional bedroom (holding the other four variables constant).

B. On average, the selling price of a house will increase by approximately $2,408 for an additional bedroom (holding the other four variables constant).

C. On average, the selling price of a house will increase by approximately $9,467 for an additional bedroom (holding the other four variables constant).

D. On average, the selling price of a house will decrease by approximately $9,467 for an additional bedroom (holding the other four variables constant).

Question 7:

Which of the following interpretations of the coefficient on the “Pool (dummy)” variable is correct?

A. On average, the selling price of a house will increase by approximately $153,678 if the house has a pool (holding the other four variables constant)

B. On average, the selling price of a house will increase by approximately $2,408 if the house has a pool (holding the other four variables constant).

C. On average, the selling price of a house will increase by approximately $22,453 if the house has a pool (holding the other four variables constant).

D. On average, the selling price of a house will decrease by approximately $22,453 if the house has a pool (holding the other four variables constant).

Question 8:

Suppose that we had information on a homeowner’s last name and included the number of letters of the last name as a sixth independent variable to the regression (i.e., there would be the five independent variables from the previous regression plus the number of letters in the last name). Which of the following is correct?

A. R-Squared would decrease since the number of letters in the owner’s last name has nothing to do with the selling price.

B. R-Squared would not change.

C. While the number of letters in the owner’s last name has nothing to do with the selling price, R-Squared would increase anyway, suggesting that the new regression is better, when it really isn’t.

D. There is not enough information to answer this question.

Answer will be sent on email. Excel file with regression analysis will also be sent.

Due Saturday August 1, 11:59 PM

Assignment 3

NOTE: THERE IS AN EXCEL FILE THAT GOES ALONG WITH THIS ASSIGNMENT. YOU NEED IT TO COMPLETE THE ASSIGNMENT.

Question 1:

Which of the following phrases makes this a correct statement: “If the covariance between two variables is negative, then …

A. … the correlation coefficient will be greater than 1.”

B. … we know for sure that the correlation coefficient between those two variables is also negative.”

C. … the variance of at least one of the variables must be negative”

D. None of the above

Question 2:

Which of the following phrases makes this a correct statement: “If the correlation coefficient between two variables is -1, then …

A. … there is no relationship at all between those two variables.”

B. … all the data points are on a straight line whose slope must be -1.”

C. … all the data points are on a straight line whose slope can be any number (positive or negative).”

D. … all the data points are on a straight line. We do not know what the exact value of the slope is, but we know that the slope is a negative number.”

Question 3:

GENERAL NOTE: Questions 3 through 5 are all based on this first regression.

The “Excel File for Test 3" (also posted under Assignments) contains information about the selling price of houses as well as related information about the houses. Please open the file in Excel and run a regression in which “Selling Price” is your Y input and “Number of Bedrooms” is your X input. Instructions on how to do that are in the Chapter 13 Notes.

Using your regression results, what is the (rounded) value of the estimated intercept “a”?

A. $161,119

B. $15,797

C. $11,716

D. $13.75

Question 4:

What is the value of the estimated slope “b”?

A. $161,119

B. $15,797

C. $11,716

D. $13.75

Question 5:

Is the estimate of the slope statistically significant? (You may want to review the information on scientific notation in the Chapter 13 Notes before answering this question.)

A. Yes, because the p-value is less than 0.05

B. Yes, because the R-Squared is between 0 and 1.

C. No, because the estimate of the slope is smaller than the estimate of the intercept.

D. It is not possible to answer this question because the number of observations is not large enough to make that decision.

Question 6:

GENERAL NOTE: Questions 6 through 8 are all based on this second regression.

Moving to Chapter 14 material (but still using the same Excel file), run one regression with “Selling Price” as the Y input and the following five variables as X variables:

- Number of Baths

- Number of Bedrooms

- Pool (dummy) – 1 indicates “pool”; 0 indicates “no pool”

- Garage (dummy) – 1 indicates “garage”; 0 indicates “no garage”

- Distance to Town Center

Which of the following interpretations of the coefficient on the “Number of Bedrooms” variable is correct?

A. On average, the selling price of a house will increase by approximately $153,678 for an additional bedroom (holding the other four variables constant).

B. On average, the selling price of a house will increase by approximately $2,408 for an additional bedroom (holding the other four variables constant).

C. On average, the selling price of a house will increase by approximately $9,467 for an additional bedroom (holding the other four variables constant).

D. On average, the selling price of a house will decrease by approximately $9,467 for an additional bedroom (holding the other four variables constant).

Question 7:

Which of the following interpretations of the coefficient on the “Pool (dummy)” variable is correct?

A. On average, the selling price of a house will increase by approximately $153,678 if the house has a pool (holding the other four variables constant)

B. On average, the selling price of a house will increase by approximately $2,408 if the house has a pool (holding the other four variables constant).

C. On average, the selling price of a house will increase by approximately $22,453 if the house has a pool (holding the other four variables constant).

D. On average, the selling price of a house will decrease by approximately $22,453 if the house has a pool (holding the other four variables constant).

Question 8:

Suppose that we had information on a homeowner’s last name and included the number of letters of the last name as a sixth independent variable to the regression (i.e., there would be the five independent variables from the previous regression plus the number of letters in the last name). Which of the following is correct?

A. R-Squared would decrease since the number of letters in the owner’s last name has nothing to do with the selling price.

B. R-Squared would not change.

C. While the number of letters in the owner’s last name has nothing to do with the selling price, R-Squared would increase anyway, suggesting that the new regression is better, when it really isn’t.

D. There is not enough information to answer this question.

Answer will be sent on email. Excel file with regression analysis will also be sent.