The client wants to know the probability that the actual relationship between Direct Mail spending and Sales is greater than 6.5. What is this probability?
| Week | Sales | Direct Mail | Lagged Direct Mail |
| 1 | $121,230 | 9800 | 42047 |
| 2 | $212,090 | 21200 | 9800 |
| 3 | $99,980 | 561000 | 21200 |
| 4 | $429,780 | 41300 | 56100 |
| 5 | $496,370 | 26700 | 41300 |
| 6 | $316,450 | 32100 | 26700 |
| 7 | $286,980 | 52900 | 32100 |
| 8 | $496,110 | 73100 | 52900 |
| 9 | $389,080 | 69500 | 73100 |
| 10 | $787,350 | 54400 | 69500 |
| 11 | $446,310 | 8700 | 54400 |
| 12 | $389,410 | 29900 | 8700 |
| 13 | $420,040 | 24300 | 29900 |
| 14 | $629,380 | 42300 | 24300 |
| 15 | $419,370 | 82000 | 42300 |
| 16 | $740,070 | 60200 | 82000 |
| 17 | $498,730 | 48900 | 60200 |
| 18 | $621,780 | 27900 | 48900 |
| 19 | $317,620 | 37600 | 27900 |
| 20 | $427,270 | 68621 | 37600 |
This is done in MINITAB 2017
Regression Analysis: Sales versus Direct Mail, Lagged Direct Mail
The following terms cannot be estimated and were removed:
Lagged Direct Mail
Method
Categorical predictor coding (1, 0)
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 1 82966905851 82966905851 2.81 0.111
Direct Mail 1 82966905851 82966905851 2.81 0.111
Error 18 5.32280E+11 29571106519
Total 19 6.15247E+11
Model Summary
S R-sq R-sq(adj) R-sq(pred)
171963 13.49% 8.68% 0.00%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 465778 44800 10.40 0.000
Direct Mail -0.561 0.335 -1.68 0.111 1.00
Regression Equation
Sales = 465778 - 0.561 Direct Mail
Fits and Diagnostics for Unusual Observations
Obs Sales Fit Resid Std Resid
1 121230 460279 -339049 -2.04 R
3 99980 150961 -50981 -1.72 X
10 787350 435250 352100 2.10 R
R Large residual
X Unusual X
Any probability cannot be greater than 0, so the question is incorrect. I have furnished the complete details of the regression analysis.
The client wants to know the probability that the actual relationship between Direct Mail spending and Sales is greater...
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