Question

High daily temperatures and coffee sales (in hundreds of dollars) were recorded at a local Starbucks for eight randomly selected days. Results are listed in the table below. Is here a correlation between temperature and coffee sales? Use α=.05. What is the best predicted sales total for a day with a high temperature of 60° F?
x(° F) 32 39 51 60 65 72 78 81
y(hundreds of dollars) 26.2 24.8 19.7 20.0 13.3 13.9 11.4 11.2

r:
critical value:
Significant linear correlation? Yes or No?
Regression equation:
Best predicted time on 60° day:
What proportion of variation in sales is due to temperature?

Answer 1

r =-0.971

critical value value at 6 (n-2=8-2) degrees of freedom and 0.05 level of significance is - 0.707

Yes, because the value of r is less than critical value of r, hence we can conclude that there is significant linear correlation.

Regression equation: y= 36.8489 - 0.3228 x

(where y= coffee sales (in hundreds of dollars) and x= High daily temperatures)

Best predicted coffee sales on 60° day:

y= 36.8489 - 0.3228 (60)

y= 17.4818 hundreds of dollars

Thus the Best predicted coffee sales on 60° day is 17.4818 hundreds of dollars

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The 0.9426 proportion of variation in sales is due to temperature.