Need answers for questions 14, 19 and 21 only please Correlation and Simple Linear Regression V2 The present study shows data for prices per gallon of paint and the demand for each brand of paint. The sales manager at a home improvement store is interested in knowing if there is a significant relationship between the price a gallon of paint and the demand (number of gallons sold). A sample of 28 different paint brands is collected and analyzed. We will test the claim that there is no relationship between the two variables. We will compare the observed level of significance (p-value) with alpha and decide if we can conclude that there is relationship between the two variable. Brand Price per Gallon ($) Demand (Gallons) 1 59.95 276 2 38.99 611 3 26.99 779 4 40.65 521 5 41.89 466 6 54.99 154 7 35.62 539 8 42.00 387 9 24.23 630 10 55.00 169 11 36.99 578 12 30.99 678 13 29.00 612 14 69.46 105 15 51.34 290 16 49.68 143 17 54.99 300 18 95.00 49 19 85.00 40 20 38.95 567 21 65.99 80 22 70.00 94 23 72.96 77 24 63.00 198 25 47.00 382 26 45.95 376 27 41.89 490 28 30.38 634 3. In cell C4. find the covariance between the price and demand for the sample on the Data sheet. 4. 4. In cell C5, find the correlation between the price and demand for the sample on the Data sheet. 5. By assessing the values in cells C4 and C5, what can you say about the relationship between the Price of the paint and Demand? Choose your answer from the dropdown menu in cell Co. 6. Explain the answer you chose in cell C6. Choose your answer from the dropdown menu in cell C7. 7. In cell C8, find the Y-Intercept (BO) of the Regression Equation from the Data Analysis output table on the Data sheet. 8. In cell C9, find the Price (X variable) coefficient (B1) from the Data Analysis output table on the Data sheet. 9. In cell C10, find the Coefficient of Determination (R2) from the Data Analysis output table on the Data sheet. 10. In cell C11, find the Regression Sum of Squares (SSR) from the Data Analysis output table on the Data sheet. 11. In cell C12, find the Error Sum of Squares (SSE) from the Data Analysis output table on the Data sheet. 12. In cell C13, find the Total Sum of Squares (SST) from the Data Analysis output table on the Data sheet. 13. In cell C14, find the value of Coefficient of Determination (R2) using SSR and SST. 14. Explain what the value of R2 means. Choose your answer from the dropdown menu in cell C15. Answers for above except 14, 19 and 21: From above excel op, we have: Q3. Covariance = -3675.34 Q4. Correlation= -0.91499 Q.5 There is a strong negative relationship Q.6 because the correlation coefficient is negative. Q7. Bo= 950.867 Q.8 B1= -11.723 Q.9 R^2 = 0.837 Q.10 SSR = 1163337.936 Q.11 SS = 226214.17 Q. 12 SST = 1389552.107 Q.13 R^2 = SSR/SST = 0.8372 Q. 14 Need answer for this question Choose one from the following. Which one is correct? A) R^2 represents the percentage of variation in the demand that is explained by the price or B) R^2 represents the percentage of variation in the price that is explained by the demand Q.15 lowest = 24.23 Q.16 highest = 95 Q.17 Demand = (-11.723) * 50 + (950.867) = 364.717 Q.18 As price increases, demand decreases Q. 19 Choose one from the following (need answer also for this question) A) Yes, the correlation coefficient is the square root of the coefficient of determination B) Yes, the correlation coefficient is half of the coefficient of determination C) Not they are not related Q.20 p-value = 9.49 * 10^-12 Q. 21 need also answer for this one Choose one from below A. Yes, I reject the claim. There is not relationship. B. Yes, I reject the claim. There is a relationship C. No, I do not reject the claim. There is a relationship D. No, I do not reject the claim. There is not relationship Q. 22 since the p-value is less than alpha, we reject the claim
Need answers for questions 14, 19 and 21 only please
The present study shows data for prices per gallon of paint and the demand for each brand of paint. The sales manager at a home improvement store is interested in knowing if there is a significant relationship between the price a gallon of paint and the demand (number of gallons sold). A sample of 28 different paint brands is collected and analyzed. We will test the claim that there is no relationship between the two variables. We will compare the observed level of significance (p-value) with alpha and decide if we can conclude that there is relationship between the two variable.
| Brand | Price per Gallon ($) | Demand (Gallons) |
| 1 | 59.95 | 276 |
| 2 | 38.99 | 611 |
| 3 | 26.99 | 779 |
| 4 | 40.65 | 521 |
| 5 | 41.89 | 466 |
| 6 | 54.99 | 154 |
| 7 | 35.62 | 539 |
| 8 | 42.00 | 387 |
| 9 | 24.23 | 630 |
| 10 | 55.00 | 169 |
| 11 | 36.99 | 578 |
| 12 | 30.99 | 678 |
| 13 | 29.00 | 612 |
| 14 | 69.46 | 105 |
| 15 | 51.34 | 290 |
| 16 | 49.68 | 143 |
| 17 | 54.99 | 300 |
| 18 | 95.00 | 49 |
| 19 | 85.00 | 40 |
| 20 | 38.95 | 567 |
| 21 | 65.99 | 80 |
| 22 | 70.00 | 94 |
| 23 | 72.96 | 77 |
| 24 | 63.00 | 198 |
| 25 | 47.00 | 382 |
| 26 | 45.95 | 376 |
| 27 | 41.89 | 490 |
| 28 | 30.38 | 634 |
3. In cell C4. find the
4. In cell C5, find the correlation between the price and demand for the sample on the Data sheet.
5. By assessing the values in cells C4 and C5, what can you say about the relationship between the Price of the paint and Demand? Choose your answer from the dropdown menu in cell Co.
6. Explain the answer you chose in cell C6. Choose your answer from the dropdown menu in cell C7.
7. In cell C8, find the Y-Intercept (BO) of the Regression Equation from the Data Analysis output table on the Data sheet.
8. In cell C9, find the Price (X variable) coefficient (B1) from the Data Analysis output table on the Data sheet.
9. In cell C10, find the Coefficient of Determination (R2) from the Data Analysis output table on the Data sheet.
10. In cell C11, find the Regression Sum of Squares (SSR) from the Data Analysis output table on the Data sheet.
11. In cell C12, find the Error Sum of Squares (SSE) from the Data Analysis output table on the Data sheet.
12. In cell C13, find the Total Sum of Squares (SST) from the Data Analysis output table on the Data sheet.
13. In cell C14, find the value of Coefficient of Determination (R2) using SSR and SST.
14. Explain what the value of R2 means. Choose your answer from the dropdown menu in cell C15.
Answers for above except 14, 19 and 21:
From above excel op, we have:
Q3. Covariance = -3675.34
Q4. Correlation= -0.91499
Q.5 There is a strong negative relationship
Q.6 because the
Q7. Bo= 950.867
Q.8 B1= -11.723
Q.9 R^2 = 0.837
Q.10 SSR = 1163337.936
Q.11 SS = 226214.17
Q. 12 SST = 1389552.107
Q.13 R^2 = SSR/SST = 0.8372
Q. 14 Need answer for this question
Choose one from the following. Which one is correct?
A) R^2 represents the percentage of variation in the demand that is explained by the price
or B) R^2 represents the percentage of variation in the price that is explained by the demand
Q.15 lowest = 24.23
Q.16 highest = 95
Q.17 Demand = (-11.723) * 50 + (950.867) = 364.717
Q.18 As price increases, demand decreases
Q. 19 Choose one from the following (need answer also for this question)
A) Yes, the correlation coefficient is the square root of the coefficient of determination
B) Yes, the correlation coefficient is half of the coefficient of determination
C) Not they are not related
Q.20 p-value = 9.49 * 10^-12
Q. 21 need also answer for this one
Choose one from below
A. Yes, I reject the claim. There is not relationship.
B. Yes, I reject the claim. There is a relationship
C. No, I do not reject the claim. There is a relationship
D. No, I do not reject the claim. There is not relationship
Q. 22 since the p-value is less than alpha, we reject the claim.
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