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.
| 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 |
following model to these data:
Yt = a + b1Yt−1 + b2Pt + et
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.
|
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 |
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