Show all work. Let Yt be the sales during month t (in thousands of dollars) for

Question

Show all work.

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 is listed below (read in 2 columns). Use regression to fit the following model to these data:
Yt = a + b1Yt1 + 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.

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

Explanation / Answer

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.

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

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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