BA 253: Multiple Linear Regression - Fort Lewis College



BA 253: Multiple Linear Regression

A) Do advertising and weather affect sales at a local store? Assume the manager of the store has kept track of weekly sales, weekly advertising expenditures, and weekly rainfall totals (in inches).

|Sales |Ad $ |Rain |

|$15,000 |$2,000 |1.50 |

|$18,000 |$2,000 |0.10 |

|$29,000 |$4,500 |0.00 |

|$16,000 |$1,500 |0.50 |

|$12,000 |$1,000 |1.00 |

|$25,000 |$5,000 |0.00 |

|$21,000 |$2,000 |0.25 |

i) Determine the linear regression equations that predict sales using only advertising and only rain totals.

ii) Interpret both slopes.

iii) Calculate and interpret r for both equations.

iv) Predict sales if $3,000 is spent on advertising.

v) Predict sales if ¾ of an inch of rain falls during the week.

vi) Predict sales if $3,000 is spent on ads and ¾ of an inch of rain falls.

vii) Repeat vi) using the multiple linear regression equation.

viii) Interpret the multiple r and r2 values.

ix) At α = 5%, is there a linear relationship (are the data correlated)?

x) Interpret the p-values from the Excel output.

B) The owner of a small business believes that his costs are potentially affected by three factors, A, B and C. Predict cost when A = 7, B = 40, and C = 200.

|Cost |A |B |C |

|500 |6 |50 |250 |

|800 |10 |25 |100 |

|1000 |11 |15 |150 |

|700 |9 |30 |300 |

|600 |5 |45 |200 |

|400 |5 |55 |150 |

|500 |4 |35 |200 |

|700 |8 |30 |50 |

i) Run multiple linear regression on all factors.

ii) What are the multiple r value and overall p-value?

iii) Predict the cost.

iii) According to the p-values for all x-variables, which factors affect the cost and which do not?

iv) Re-run the multiple linear regression for just those factors that are significant.

v) Now what are the multiple r value and overall p-value.

vi) Predict the cost again. Which prediction is better?

|A)SUMMARYOUTPUT | | | | | |

| | | | | | |

|Regression Statistics | | | | |

|Multiple R |0.943012486 |Strong Correlation | | |

|R Square |0.88927255 | | | | |

|Adjusted R Square |0.833908824 | | | | |

|Standard Error |2432.28483 | | |P | |

|Observations |7 | | | | |

| | | | | | |

|ANOVA | | | | | |

|  |df |SS |MS |F |Significance F |

|Regression |2 |190050247.7 |95025123.87 |16.06236838 |0.012260568 |

|Residual |4 |23664037.98 |5916009.495 | | |

|Total |6 |213714285.7 |  |  |  |

| | | | | | |

|  |Coefficients |Standard Error |t Stat |P-value |Lower 95% |

|Intercept |14121.98562 |2960.339103 |4.770394582 |0.008837518 |5902.749582 |

|Ad |2.718843113 |0.804975346 |3.377548302 |0.027848514 |0.483868625 |

|Rain |-3520.3210 |2162.672384 |-1.62776434 |0.178904874 |-9524.87459 |

|B)SUMMARYOUTPUT | | | | | |

| | | | | | |

|Regression Statistics | | | | |

|Multiple R |0.960652931 |Good fit | | | |

|R Square |0.922854055 | | | | |

|Adjusted R Square |0.864994596 | | | | |

|Standard Error |70.81303864 | | | | |

|Observations |8 | | | | |

| | | | | | |

|ANOVA | | | | | |

|  |df |SS |MS |F |Significance F |

|Regression |3 |239942.1 |79980.68474 |15.94992542 |0.010867814 |

|Residual |4 |20057.95 |5014.486441 | | |

|Total |7 |260000 |  |  |  |

| | | | | | |

|  |Coefficients |Standard Error |t Stat |P-value |Lower 95% |

|Intercept |671.4323587 |246.5126 |2.723724395 |0.052783538 |-12.9977365 |

|A |35.07423118 |17.89929 |1.959531504 |0.121619958 |-14.6222799 |

|B |-7.55794576 |3.499378 |-2.15979677 |0.096911163 |-17.2737973 |

|C |-0.03696409 |0.347869 |-0.10625853 |0.920493003 |-1.00280644 |

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