A brokerage house wants to predict the number of trade executions per day, using the number of incoming phone calls as a predictor variable. Data were collected over a period of 35 days:
a. Use the least-squares method to compute the regression coefficients b0 and b1.
b. Interpret the meaning of b0 and b1 in this problem.
c. Predict the number of trades executed for a day in which the number of incoming calls is 2,000.
d. Should you use the model to predict the number of trades executed for a day in which the number of incoming calls is 5000? Why or why not?
e. Determine the coefficient of determination, r^2, and explain its meaning in this problem.
i. At the 0.05 level of significance, is there evidence of a linear relationship between the volume of trade executions and the number of incoming calls?
j. Construct a 95% confidence interval estimate of the mean number of trades executed for days in which the number of incoming calls is 2000.
k. Construct a 95% prediction interval of the number of trades executed for a particular day in which the number of incoming calls is 2000.
Step by step method for regression analysis is discussed here. Regression coefficients, coefficient of determination, scatter diagram and significance of regression model are explained in the solution.