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A simple linear regression equation, LNQ = a + bLNH + cLNS is estimated by a...

  1. A simple linear regression equation, LNQ = a + bLNH + cLNS is estimated by a computer regression routine which produces the following output – see the information below. LNQ is the percentage change in the number of cars sold in a day; LNH is the percentage change in the number hours the dealership is open; and LNS is the percentage change in the number of sales persons working that day. The parameter estimates can be interpreted as the percentage change in sales due a percentage change in the independent variable.
    1. How many degrees of freedom does this regression analysis have?
    2. What is the critical value of t at the 5 percent level of significance?
      1. Test to see if the estimates of a, b and c are statistically significant.
    3. How much of the total variation in LNQ is explained by this regression equation? How much of the total variation in LNQ is unexplained by this regression equation?
    4. What is the critical value of the F-statistic at a 5 percent level of significance?
      1. Is the overall regression equation statistically significant?
    5. If the number of sales people (LNS) is increased by 10% by how much should sales rise
      Dependent Variable:         LNQ       R-Square               F-Ratio                  p-Value of F

        Observations        53                           0.5452                   29.97                      .0001

Variable                 Parameter              Standard                T- Ratio                 p-value

                                        Estimate                Error

        Intercept                0.9162                   .2413                      3.80                        .0004

        LNH                       0.3517                   .1021                      3.44                        .0012

        LNS                        0.2550                   .0785                      3.25                        .0021

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Answer:

  1. A simple linear regression equation, LNQ = a + bLNH + cLNS is estimated by a computer regression routine which produces the following output – see the information below. LNQ is the percentage change in the number of cars sold in a day; LNH is the percentage change in the number hours the dealership is open; and LNS is the percentage change in the number of sales persons working that day. The parameter estimates can be interpreted as the percentage change in sales due a percentage change in the independent variable.
    1. How many degrees of freedom does this regression analysis have?

Total Df= n-1=52

Regression Df= 2

Error Df= 50

  1. What is the critical value of t at the 5 percent level of significance?

Critical t=2.009

Test to see if the estimates of a, b and c are statistically significant.

To test for a, calculated t=3.80   > 2.009 the critical value, a is significant.

To test for b, calculated t=3.44   > 2.009 the critical value, b is significant.

To test for c, calculated t=3.25   > 2.009 the critical value, c is significant.

  1. How much of the total variation in LNQ is explained by this regression equation? How much of the total variation in LNQ is unexplained by this regression equation?

R square =0.5452. 54.52% of variation in LNQ is explained by this regression equation.

45.48% of variation in LNQ is unexplained by this regression equation

  1. What is the critical value of the F-statistic at a 5 percent level of significance?

Is the overall regression equation statistically significant?

Critical F( 2,50) = 3.183

calculated F=29.97   > 3.183 the critical F value, regression equation is significant.

  1. If the number of sales people (LNS) is increased by 10% by how much should sales rise

Regression coefficient for LNS= 0.2550

For a 10% increase in LNS, there is a 2.55% in sales increase.


  1. Dependent Variable:         LNQ       R-Square               F-Ratio                  p-Value of F

        Observations        53                           0.5452                   29.97                      .0001

Variable                 Parameter              Standard                T- Ratio                 p-value

                                        Estimate                Error

        Intercept                0.9162                   .2413                      3.80                        .0004

        LNH                       0.3517                   .1021                      3.44                        .0012

        LNS                        0.2550                   .0785                      3.25                        .0021

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