An ice-cream shop wants to model the relationship between ice cream sales and temperature. They collect data on temperature (in Fahrenheit) and sales (in dollars) for twenty summer days. Let x be the variable for temperature, and y be the variable for sales. The estimated regression line is

y^_i= 352.517 + 3.153x_i

(a) The average temperature across the twenty days was 79.515. What was the average in ice cream sales across the twenty days?

(b) According to the model, how much ice cream sales are expected on a day with 81 degree weather?

(c) On day 5, the temperature was 85.9 degrees, and the shop made $628.41 in ice cream sales. What is the value of the residual for this observation? Were sales that day better than expected, or worse than expected, based on the model?

(d) The estimated standard error of the slope is ˆse(βˆ1) = 1.524. Perform a t-test of hypotheses

H0 : β1 = 0 versus HA : β1(not=)0

with α = 0.01 to test whether there is a relationship between temperature and ice cream sales. Interpret your findings in the context of the question.

Answer rating: 100% (QA)

a The average ice cream sales across the twenty days was 1781340 This means that on average the ice ... View the full answer