Question

The following estimated regression equation relating sales to inventory investment and advertising expenditures was given.

ŷ = 24 + 12x₁ + 7x₂

The data used to develop the model came from a survey of 10 stores; for those data, SSyy (Total Sum of Squares) = 17,000 and SSR (Regression Sum of Squares) = 12,070.

(a)For the estimated regression equation given, compute R².(Round your answer to two decimal places.)

R² =

(b) Compute the adjusted r-square, R_a².(Round your answer to two decimal places.)

R_a² =

(c) Does the model appear to explain a large amount of variability in the data? Explain. (For purposes of this exercise, consider an amount large if it is at least 55%. Round your answer to the nearest integer.)

The adjusted coefficient of determination shows that ______ % of the variability has been explained by the two independent variables; thus, we conclude that the model (does /does not) explain a large amount of variability.

Answer 1

(a)

(b) Here n = number of data points = 10

p = number of predictor variables = 2

(c)

Does the model appear to explain a large amount of variability in the data? Explain. (For purposes of this exercise, consider an amount large if it is at least 55%. Round your answer to the nearest integer.)

Since -squared value is 0.71 it denotes the explanatory variable explains 71% of the variability greater than 55%. Thus we can conclude that the model appears to explain a large amount variability in the data.

The adjusted coefficient of determination shows that 63% of the variability has been explained by the two independent variables; thus, we conclude that the model does explain a large amount of variability