Suppose the Sherwin-Williams Company is interested in developing a simple regression model with paint sales (Y) as the dependent variable and selling price (P) as the independent variable. Complete the following worksheet and then use it to determine the estimated regression line. Sales Region Selling Price Sales ($/Gallon) (x 1000 Gal) ii xixi yiyi xixiyiyi xi2xi2 yi2yi2 1 15 160 2,400 225 25,600 2 13.5 220 2,970 182.25 48,400 3 16.5 140 2,310 272.25 19,600 4 14.5 190 2,755 210.25 36,100 5 17 120 2,040 289 14,400 6 16 160 2,560 256 25,600 7 13 210 2,730 169 44,100 8 18 150 2,700 324 22,500 9 12 220 2,640 144 48,400 10 15.5 190 2,945 240.25 36,100 Total 151 1,760 26,050 2,312 320,800 Regression Parameters Estimations Slope (ββ) -16.49 Intercept (αα) 424.98 In words, for a dollar increase in the selling price, the expected sales will increase by 2,640 gallons in a given sales region. What is the standard error of the estimate (sese)? 17.200 What is the estimate of the standard deviation of the estimated slope (sbsb)? 3.045
Suppose the Sherwin-Williams Company is interested in developing a simple regression model with paint sales (Y) as the dependent variable and selling price (P) as the independent variable. Complete the following worksheet and then use it to determine the estimated regression line. Sales Region Selling Price Sales ($/Gallon) (x 1000 Gal) ii xixi yiyi xixiyiyi xi2xi2 yi2yi2 1 15 160 2,400 225 25,600 2 13.5 220 2,970 182.25 48,400 3 16.5 140 2,310 272.25 19,600 4 14.5 190 2,755 210.25 36,100 5 17 120 2,040 289 14,400 6 16 160 2,560 256 25,600 7 13 210 2,730 169 44,100 8 18 150 2,700 324 22,500 9 12 220 2,640 144 48,400 10 15.5 190 2,945 240.25 36,100 Total 151 1,760 26,050 2,312 320,800 Regression Parameters Estimations Slope (ββ) -16.49 Intercept (αα) 424.98 In words, for a dollar increase in the selling price, the expected sales will increase by 2,640 gallons in a given sales region. What is the standard error of the estimate (sese)? 17.200 What is the estimate of the standard deviation of the estimated slope (sbsb)? 3.045
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Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Question
Suppose the Sherwin-Williams Company is interested in developing a simple regression model with paint sales (Y) as the dependent variable and selling price (P) as the independent variable.
Complete the following worksheet and then use it to determine the estimated regression line.
|
Sales Region
|
Selling Price
|
Sales
|
|
||
|---|---|---|---|---|---|
|
($/Gallon)
|
(x 1000 Gal)
|
||||
| ii | xixi | yiyi | xixiyiyi | xi2xi2 | yi2yi2 |
| 1 | 15 | 160 | 2,400 | 225 | 25,600 |
| 2 | 13.5 | 220 | 2,970 | 182.25 | 48,400 |
| 3 | 16.5 | 140 | 2,310 | 272.25 | 19,600 |
| 4 | 14.5 | 190 | 2,755 | 210.25 | 36,100 |
| 5 | 17 | 120 | 2,040 | 289 | 14,400 |
| 6 | 16 | 160 | 2,560 | 256 | 25,600 |
| 7 | 13 | 210 | 2,730 | 169 | 44,100 |
| 8 | 18 | 150 | 2,700 | 324 | 22,500 |
| 9 | 12 | 220 | 2,640 | 144 | 48,400 |
| 10 | 15.5 | 190 | 2,945 | 240.25 | 36,100 |
| Total | 151 | 1,760 | 26,050 | 2,312 | 320,800 |
|
Regression Parameters
|
Estimations
|
|---|---|
| Slope (ββ) | -16.49 |
| Intercept (αα) | 424.98 |
In words, for a dollar increase in the selling price, the expected sales will increase by 2,640 gallons in a given sales region.
What is the standard error of the estimate (sese)?
17.200
What is the estimate of the standard deviation of the estimated slope (sbsb)? 3.045
Can you reject the hypothesis (at the 0.05 level of significance) that there is no relationship (i.e., β=0β=0) between the variables? (Hint: t0.025,8=2.306t0.025,8=2.306)
No
Yes
Complete the following worksheet and then use it to calculate the coefficient of determination.
|
ii
|
xixi
|
yiyi
|
yˆy^
|
(yˆi−y¯)2y^i−y¯2
|
(yi−y¯)2yi−y¯2
|
|---|---|---|---|---|---|
| 1 | 15 | 160 | 177.649 | 2.719 | 256.000 |
| 2 | 13.5 | 220 | 202.382 | 696.010 | 1,936.000 |
| 3 | 16.5 | 140 | 152.915 | 532.917 | 1,296.000 |
| 4 | 14.5 | 190 | 185.893 | 97.871 | 196.000 |
| 5 | 17 | 120 | 144.671 | 981.506 | 3,136.000 |
| 6 | 16 | 160 | 161.160 | 220.226 | 256.000 |
| 7 | 13 | 210 | 210.627 | 1,199.029 | 1,156.000 |
| 8 | 18 | 150 | 128.182 | 2,286.561 | 676.000 |
| 9 | 12 | 220 | 227.116 | 2,612.845 | 1,936.000 |
| 10 | 15.5 | 190 | 169.404 | 43.507 | 196.000 |
| Total | ? | ? |
The coefficient of determination (r2r2) is?
According to the regression model, which of the following is the best estimate together with the 95 percent prediction interval of paint sales (in thousands of gallons) in a sales region where the selling price is $12.50?
437.605 ± 2(17.200)
218.855 ± 2(17.200)
437.605 ± 2(3.045)
218.855 ± 2(3.045)
What is the price elasticity of demand at a selling price of $12.50?
-0.58
-0.07
-0.94
-0.06
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