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Regression

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Submitted By robingeorge
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Q1: All the regressions were performed. Output can be made available if needed. See outputs for Q2 in appendix. Q2: Select the model you are going to keep for each brand and explain WHY. Report the corresponding output in an appendix attached to your report (hence, 1 output per brand)

We use Adjusted R Squared to compare the Linear or Semilog Regression. R^2 is a statistic that will give some information about the goodness of fit of a model. In regression, the Adjusted R^2 coefficient of determination is a statistical measure of how well the regression line approximates the real data points. An R2 of 1 indicates that the regression line perfectly fits the data.

Brand1:

Linear Regression R^2 | 0.594 | SemiLog Regression R^2 | 0.563 |

We use the Linear Regression Model since R-squared is higher.

Brand 2: Linear Regression R^2 | 0.758 | SemiLog Regression R^2 | 0.588 |

We use the Linear Regression Model since R-squared is higher

Brand 3:

Linear Regression R^2 | 0.352 | SemiLog Regression R^2 | 0.571 |

We use the Semilog Regression Model since R-squared is higher

Brand 4: Linear Regression R^2 | 0.864 | SemiLog Regression R^2 | 0.603 |

We use the Linear Regression Model since R-squared is higher

Q3: Here we compute the cross-price elasticity. Depending on whether we use linear or semi-log model,

Linear Model
Linear Model

Semi-Log Model
Semi-Log Model `

| Brand 1 | Brand 2 | Brand 3 | Brand 4 | Mean Price | 1.117 | 1.006 | 0.963 | 0.838 | Mean Sales | 541.79 | 218.58 | 137.19 | 109.30 |

For example, Brand 2’s price effect on Brand 1’s sales, will be computed as

η=0*1.006541.79=0

Brand 2’s price effect on Brand 4’s sales will be computed as...

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