Malaple Resn 1. The Campus Bike Shop, located near the campus of a large uni- ve

ID: 3372112 • Letter: M

Question

Malaple Resn 1. The Campus Bike Shop, located near the campus of a large uni- versity, sells and repairs bicycles of all types. The owner has been in the habit of ordering the same number of 10-speed bicycles each month, but the result has been overstockage in some months and the loss of sales because of lack of inventory in other months. As a consultant, you propose to predict monthly sales by the linear regression equation where Q Estimated monthly sales x, = Average selling price, in dollars X2 Average price of lead-free gasoline, in dollars X, 1 if fall semester, otherwise zero x, = 1 if spring semester, otherwise zero (X,-0 and X4 = 0 implies summer term) Using the data from the past 15 months, you obtain the following results from a linear regression program on a computer STD VARIABLE COEFF ERROR T-VALUE -0.6041.33 77.44 42.84 14.83 22.64 38.91 16.18 14.39 59.59 -0.45 1.99 2.65 1.03 0.38 2 INTERCEPT R-SQUARED 636 STANDARD ERROR 4.4 F-VALUE-8.14 Write the estimated regression equation and interpret the estimated a. b. c. coefficients. Test the regression equation for overall significance at the .05 level. Interpret the coefficient of determination.

Explanation / Answer

Answer:

Part a

From given output for the linear regression program, the estimated regression equation is given as below:

Q = 22.64 – 0.604*X1 + 77.44*X2 + 42.84*X3 + 14.83*X4

Now, we have to interpret the estimated coefficients. First we have to find the p-values for given coefficients. P-values are calculated by using t-table or excel. P-values are given as below:

Total number of observations = n = 15, so df = n – 1 = 14

Variable

Coeff.

T-value

P-value

-0.604

-0.45

0.3404

77.44

1.99

0.0665

42.84

2.65

0.0190

14.83

1.03

0.3205

Intercept

22.64

0.38

0.7096

P-value for third variable (X3) is given as 0.0190 < alpha value 0.05, so this variable is statistically significant at 0.05 level of significance. Remaining variables are not statistically significant at 5% level of significance.

Part b

Test statistic for overall significance of the regression model is given as below:

F = 8.14

Total number of observations = n = 15

Number of variables = m = 4

So, df1 = m – 1 = 4 – 1 = 3

Total df = n – 1 = 15 – 1 = 14

df2 = total df – df1 = 14 – 3 = 11

With F = 8.14, df1 = 3, df2 = 11, we have

P-value = 0.003899

(By using F-table or excel)

P-value < alpha value 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that given regression model is statistically significant at 0.05 level of significance.

Part c

The value for coefficient of determination or R square is given as 0.636, which means about 63.6% of the variation in the dependent variable or response variable estimated monthly sales (Q) is explained by the independent variables X1, X2, X3, and X4.