Question

The data below represents an international corporation’s internal estimates of sales (in thousands of dollars) in the coming year over time (in weeks). Use a linear regression to model the data. Round all your coefficients to three decimal places. Then use a residual plot to determine if your model is a good fit.
Week (x) Sales (y)
(in thousands of dollars)
11 1024910249
22 1184011840
33 1193611936
44 1231012310
55 1353613536
66 1452414524
77 1392613926
88 1529315293
99 1610016100
1010 1664316643
1111 1623816238
Answer
Attempt 1 out of 2

Model: yy =

The model
a good fit because
.

Answer 1

Model (rounded to 3 decimals):
ŷ = 10162.909 + 618.227 x

Residuals (y − ŷ), rounded to 3 decimals:
x=1: −532.136
x=2: 440.636
x=3: −81.591
x=4: −325.818
x=5: 281.955
x=6: 651.727
x=7: −564.500
x=8: 184.273
x=9: 373.045
x=10: 297.818
x=11: −725.409

Conclusion from the residual plot:
The residuals are scattered above and below zero with no obvious systematic curve or trend, so a linear model appears reasonable. (There are a few moderately large residuals at some weeks, but no clear pattern that would indicate a non‑linear model is required.)