Question: The owner of a small factory that produces working gloves is concerned about the high cost of air conditioning in the summer but is afraid that keeping the temperature in the factory too high will lower productivity. During the summer, he experiments with temperature settings from 68ºF to 81ºF and measures each day's productivity. The following table gives the temperature and the number of pairs of gloves (in hundreds) produced on each of the 8 randomly selected days.

a. Do the pairs of gloves produced depend on temperature, or does temperature depend on pairs of gloves produced? Do you expect a positive or a negative relationship between these two variables?

b. Taking temperature as an independent variable and pairs of gloves produced as a dependent variable, compute SSxx, SSyy, and SSxy.

c. Find the least squares regression line.

d. Interpret the meaning of the values of a and b calculated in part c.

e. Plot the scatter diagram and the regression line.

f. Calculate r and r2 , and explain what they mean.

g. Compute the standard deviation of errors.

h. Predict the number of pairs of gloves produced when x = 74.

i. Construct a 99% confidence interval for B.

j. Test at the 5% significance level whether B is negative.

k. Using α = .01 can you conclude that is negative?