Question

Following estimated regression equation relabng sales to inventory investment and advertising expenditures was given:

ϕ=27+14x₁​+6x₂

The data used to develop the model came from a survey of 10 stores; for those data, SST =17,000 and SSR =12.410. For the estimated regression equation given, compute R².
A² = ?

Answer 1

The coefficient of determination (R²) for the estimated regression equation is obtained by dividing the Sum of Squares due to Regression (SSR) by the Total Sum of Squares (SST), which in this case equals 0.7294 or 72.94%.

Step-by-step explanation:

To compute R², also known as the coefficient of determination, for the estimated regression equation ϕ=27+14x₁+6x₂, we make use of the given Total Sum of Squares (SST) and the Sum of Squares due to Regression (SSR). The formula for R² is given as SSR divided by SST:

R² = SSR / SST

Inserting the provided values yields:

R² = 12,410 / 17,000

This simplifies to R² = 0.7294 or 72.94% when expressed as a percentage. This means that approximately 72.94% of the variability in sales is explained by the variability in inventory investment and advertising expenditures.