An ice cream vendor would like to predict daily sales of ice cream cones based on the temperature outdoors. Data for a random sample of 8 days are provided in the table below.
Temperature (°C) (x)
6, 8, 12, 16, 18, 22, 28, 28,
Daily Sales (Litres) (y)
135, 50, 125, 100, 200, 150, 250, 175,
A) Interpret the value of b in the sample regression line. What does it mean in the context of this question?
B) Compute the linear correlation between "daily sales" and "temperature." Note: Express your answer to 4 decimal places of accuracy.
C) At the 5% significance level, can it be concluded that the correlation between daily sales and temperature is positive? Formulate and test the appropriate hypotheses. Use the critical value approach.
D) What percentage of the variation in daily sales is explained by its linear relationship with temperature?
E) Using the regression line and sums of squares and cross products provided above, construct a 90% prediction interval for daily sales when the outside temperature is 24°C.