Question 2Please show your work withexplanationsto make it understandable

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 ( degree C) Daily Sales (Litres)

(x) (y)

6 135

8 50

12 125

16 100

18 200

22 150

28 250

28 175

The regression line with daily sales as the dependent variable andtemperature as the independent variable has been calculated as:

y 55.217+ 5.38597 x

You may use the following sums of squares and cross products for the questions below.

SIGMAx=138 SIGMAy=1185

SSxx=495.5 SSyy=26446.875 SSxy= 2668.75

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 andtemperature.

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 degree C.