Question
In: Statistics and Probability
The data below represent a firm’s dollars spent on advertising for a sample of 4 months...
The data below represent a firm’s dollars spent on advertising for a sample of 4 months and the firm’s sales (in units sold) for those months.
| month | advertising expenditures (x) | units sold (y) |
| 1 | $2215 | 543 |
| 2 | $2975 | 664 |
| 3 | $2150 | 538 |
| 4 | $2060 | 575 |
1. What is the correct interpretation of the coefficient of
determination?
2. What are expected sales if advertising spending is $3000?
3. What is the size of the error term for month 1?
4. Because the OLS method was used, what can be said about the fit of this line to the scatterplot of data?
Solutions
Expert Solution
| x | y | (x-x̅)² | (y-ȳ)² | (x-x̅)(y-ȳ) |
| 2215 | 543 | 18225.00 | 1369.00 | 4995.00 |
| 2975 | 664 | 390625.00 | 7056.00 | 52500.00 |
| 2150 | 538 | 40000.00 | 1764.00 | 8400.00 |
| 2060 | 575 | 84100.00 | 25.00 | 1450.00 |
| ΣX | ΣY | Σ(x-x̅)² | Σ(y-ȳ)² | Σ(x-x̅)(y-ȳ) | |
| total sum | 9400 | 2320 | 532950 | 10214.0 | 67345.00 |
| mean | 2350.00 | 580.00 | SSxx | SSyy | SSxy |
1)
R² = (Sxy)²/(Sx.Sy) = 0.8332
interpretation : it says that 83.32% (0.8332) data is explained by the explainatory varible of X of response variable Y
..................
2)
Predicted Y at X= 3000
is
Ŷ = 283.04766 +
0.126363 * 3000 =
662.136
............
3)
Ŷ for month 1 =562.941
residual,ei=y-yhat =-19.941
error = (Y-Ŷ)²
=397.64
............
It is good fit data..strong linear relationship
please revert back for doubt
orchestra answered 1 year agoRelated Solutions
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