In order to investigate what determines the export sales (measured in pounds,) o

Question

In order to investigate what determines the export sales (measured in pounds,) of 109 companies a researcher created a regression model that included the following four independent variables: the size of a company (measured as the number of employees - variable named "Employees "); whether a company collaborated with other firms (measured by a qualitative dummy variable where 1 = Have collaborated,0 = Have not collaborated - variable named "Cooperation "); company's age (measured in years - variable named Age) and the amount of income a company generated from the sale of innovative products (measured in pounds, - variable named " Innovation Sales ") Write down the equation for companies export sales as a function of the number of employees, a company's age, whether a company has collaborated with other firms and income generated from products. Then use the equation to predict the export sales of a company that has 20 employees is 5 years old, has collaborated with other and has innovative sales equal to 50000. Interpret the equation from part a in the following ways: First in terms of the direction and of the effect that each independent variable (employees, age, cooperation and innovation sales) has on the dependent variable, and Second in terms of the statistical significance (including discussion on the level of significance) of each one of the independent variables. Interpret square or the R squared value (whichever you think is most appropriate). Based on this interpretation would you recommend the usage of this model in order to make predictions for a company's export sales? How can you further improve the model? Put the independent variables in an order starting from the one that has the highest effect on export sales and finishing with the one that has the lowest effect. Justify your answer. In the two tables below you can find the correlation matrix between the dependent and the independent variables and the last part of the coefficients table from the SPSS output. Do you think that the model suffers from multicollinearity? Justify answer by using evidence from both tables. lf you think multicollinearity is a problem how would you treat it?

Explanation / Answer

Part a

First of all we have to write the regression equation from the given regression output. The regression equation is given as below:

Export sales Y = 1197515.93 – 6241.71*Employees + 9105.20*Cooperation + 19327.35*Age + 2.250*Innovation sales

Y = 1197515.93 – 6241.71*X1 + 9105.20*X2 + 19327.35*X3 + 2.250*X4

Now, we have to find the predicted export sales for the given values of independent variables.

Y = 1197515.93 – 6241.71*X1 + 9105.20*X2 + 19327.35*X3 + 2.250*X4

Y = 1197515.93 – 6241.71*20 + 9105.20*1 + 19327.35*5 + 2.250*50000

Y = 1290924

Predicted export sales = €1290924

Part b

The direction of variable employees is negative while direction of other independent variables cooperation, age and innovation sales is positive. The variable employees have negative impact on the export sales while other variables have positive impact on export sales.

With regarding the statistical significance, the p-value for the t test for coefficient of variable employees is given as 0.055 which means this coefficient is not statistically significant at 5% level of significance. The p-value for coefficient of variable cooperation is given as 0.416 which indicate that this coefficient is not statistically significant at 5% level of significance. The P-values for age and innovation sales are less than 0.05, hence these two variables are statistically significant at 5% level of significance.

Part c

The value for the adjusted R squared value is given as 0.70 which means about 70% of the variation in the dependent variable export sales is explained by the independent variables employees, cooperation, age and innovation sales. For getting better predictions for the export sales, we can include some other independent variables which are most correlated and we can ignore or delete the statistically insignificant variables.

Part d

The independent variables with highest P-value have lowest effect. The variables with highest effect to lowest effect are given as below:

Innovation sales (0.000)...............(Highest effect)

Age (0.034)

Employees (0.055)

Cooperation (0.416)......................(Lowest effect)

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