Question
In: Statistics and Probability
23-64) Let Yt be the sales during month t (in thousands of dollars) for a photography...
23-64) Let Yt be the sales during
month t (in thousands of dollars) for a photography
studio, and let Pt be the price charged for portraits
during month t. The data are in the file Week 4 Assignment
Chapter 12 Problem 64. Use regression to fit the following model to
these data:
Yt = a + b1Yt−1 + b2Pt + et
This equation indicates that last month’s sales and the current
month’s price are explanatory variables. The last term, et, is an
error term. Show all work.
- If the price of a portrait during month 21 is $10, what would you predict for sales in month 21?
- Does there appear to be a problem with autocorrelation of the residual? Explain your answer
Data:
| Sales | Price |
| $400,000 | $15 |
| $1,042,000 | $12 |
| $1,129,000 | $24 |
| $1,110,000 | $18 |
| $1,336,000 | $18 |
| $1,363,000 | $30 |
| $1,177,000 | $27 |
| $603,000 | $24 |
| $582,000 | $36 |
| $697,000 | $27 |
| $586,000 | $24 |
| $673,000 | $27 |
| $546,000 | $30 |
| $334,000 | $33 |
| $27,000 | $24 |
| $76,000 | $27 |
| $298,000 | $30 |
| $746,000 | $18 |
| $962,000 | $21 |
| $907,000 | $24 |
Solutions
Expert Solution
Regression Analysis: Sales versus Sales(t-1), Price
The
regression equation is
Sales = 589667 + 0.741 Sales(t-1) - 16124 Price
Predictor Coef SE Coef T P
Constant 589667 268264 2.20 0.042
Sales(t-1) 0.7412 0.1486 4.99 0.000
Price -16124 9506 -1.70 0.108
S = 252212 R-Sq = 63.0% R-Sq(adj) = 58.7%
If the price of a portrait during month 21 is $10, what would you predict for sales in month 21?
Does there appear to be a problem with autocorrelation of the residual? Explain your answer.
Ans: The price of a portrait during month 21 is $10, then the predict for sales in month 21
Sales = 589667 + 0.741 *907,000 - 16124 *10 = $1141269.
There is no autocorrelation between the error. Hence, there is no problem.
| Sales(Y(t)) | Sales(Y(t-1)) | Price |
| $400,000 | mean(Y(t)) | $15 |
| $1,042,000 | $400,000 | $12 |
| $1,129,000 | $1,042,000 | $24 |
| $1,110,000 | $1,129,000 | $18 |
| $1,336,000 | $1,110,000 | $18 |
| $1,363,000 | $1,336,000 | $30 |
| $1,177,000 | $1,363,000 | $27 |
| $603,000 | $1,177,000 | $24 |
| $582,000 | $603,000 | $36 |
| $697,000 | $582,000 | $27 |
| $586,000 | $697,000 | $24 |
| $673,000 | $586,000 | $27 |
| $546,000 | $673,000 | $30 |
| $334,000 | $546,000 | $33 |
| $27,000 | $334,000 | $24 |
| $76,000 | $27,000 | $27 |
| $298,000 | $76,000 | $30 |
| $746,000 | $298,000 | $18 |
| $962,000 | $746,000 | $21 |
| $907,000 | $962,000 | $24 |
In excell,
1. Select "Data".
2. Select " Data Analysis"
3. Select "Regression"
4. Put Y(t) at "Input Y range.
5. Put Y(t-1) and Price at "Input X range".
6. Click OK
orchestra answered 2 years agoRelated Solutions
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