Question

2. the cotton mill is an upscale chain of women’s clothing stores. Located in the southwestern united states. Do to recent success, the cotton mill’s top management is planning to expand by locating new stores in other regions of the country. The director of planning has been asked to study the relationship between yearly sales and the store size. As part of the study, the director selects sample of 25 stores and determines the size of the store in square feet and the sales for the last year. The sample data follows.  

	Store size (1000s of square feet)	Sales (Million of $)
1	3.7	9.18
2	2.0	4.58
3	5.0	8.22
4	0.7	1.45
5	2.6	6.51
6	2.9	2.82
7	5.2	10.45
8	5.9	9.94
9	3.0	4.43
10	2.4	4.75
11	2.4	7.30
12	0.5	3.33
13	5.0	6.67
14	0.4	0.55
15	4.2	7.56
16	3.1	2.23
17	2.6	4.49
18	5.2	9.90
19	3.3	8.93
20	3.2	7.60
21	4.9	3.71
22	5.5	5.47
23	2.9	8.22
24	2.2	7.17
25	2.3	4.35

a.       The regression model is?

b.       interpret the regression constant and regressioncoeffient?

c.       Forecast a value for the dependent variable

d.       Test the significant of the regression coefficient using apha=0.05

e.       Test the overall significant of the regression model.

f.        Interpret the coefficient of determination

g.       Are there any indications of a violation of the general linear model? Be specific.

Answer 1

The regression analysis is done in excel by following steps

Step 1: Write the data values in excel. The screenshot is shown below,

Step 2: DATA > Data Analysis > Regression > OK. The screenshot is shown below,

Step 3: Select Input Y Range: 'y' column, Input X Range: 'x' column then OK. The screenshot is shown below,

The result is obtained. The screenshot is shown below,

a)

The Simple linear regression equation is

b)

c)

Let X = 5.4,

d)

The significance of the regression coefficient is determined bu the t-statistic and the corresponding P-value.

From the result summary,

The P-value = 0.00362 is less than 0.05 at 5% significance level hence, the null hypothesis is rejected(Null hypothesis: coefficient = 0). Now we can state that there is a statistically significant effect of independent variable on dependent variable (coeficient is not equal to zero)

e)

The overall significance is determined by the ANOVA model summary obtained in the regression analysis output summary,

The Significance F-value = 0.00362 is less than 0.05 at 5% significance level hence, the null hypothesis is rejected. Now we can state that the model is statistically significant.

f)

The R square value of the model is 43.136% which means data points of independent variables explain the 43.136% of the variance of the dependent variable