Question

In: Math

1. The president of a national real estate company wanted to know why certain branches of...

1. The president of a national real estate company wanted to know why certain branches of the company outperformed others. He felt that the key factors in determining total annual sales ($ in millions) were the advertising budget (in $1000s) X1 and the number of sales agents X2. To analyze the situation, he took a sample of 25 offices and ran the following regression. The computer output is below.

            PREDICTOR            COEF             STDEV                       P-VALUE

            Constant                    -19.47             15.84                          0.2422

            X1                                0.1584            .0561                          0.0154

            X2                                0.9625            .7781                          0.2386

            Se = 7.362                             R squared = .524                             Sig F = 0.0116

(a)What are the anticipated signs for each of the independent variables in the model?

  

(b) Interpret the slope coefficient associated with the number of real estate agents.

(c) Test to determine if a positive relationship exists between the advertising spending and annual sales. Use alpha = .05.

(d) Can we conclude that this model explains a significant portion of the variation in annual sales? Use alpha =.01.

Solutions

Expert Solution

(a)

The variable X1 has positive sign. It shows that the advertising budget is positively related with the total annual sales.

The variable X2 has positive sign. It shows that the number of sales agents is positively related with the total annual sales.

(b)

The slope of variable X1 is 0.1584. That is for each unit increase in advertising budget, the sales is increased by 0.1584 units keeping other variable constant. That is for each $1000 increase in advertising budget, the sales is increased by 0.1584 millions keeping other variable constant.

The slope of variable X2 is 0.9625. That is for each one increase in number of sales person, the sales is increased by 0.9625 units keeping other variable constant.

(c)

Here we need to test following hypothesis

Since p-value of 2 tailed test is 0.0154 so p-value of one tailed test is 0.0154 / 2 = 0.0077.

Since p-value is less than  alpha = .05 so we reject the null hypothesis. That is we can conclude that a positive relationship exists between the advertising spending and annual sales.

(d)

Here we need to consider the F test. It is given that p-value of F test is 0.0116.

Since p-value is greater than alpha =.01 so we can conclude that this model explains a significant portion of the variation in annual sales.


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