Question

The following estimated regression equation based on 30 observations was presented.

ŷ = 17.6 + 3.8x₁ − 2.3x₂ + 7.6x₃ + 2.7x₄

The values of SST and SSR are 1,807 and 1,758, respectively.

(a)

Compute R². (Round your answer to three decimal places.)

R² =

(b)

Compute

R_a².

(Round your answer to three decimal places.)

R_a² =

part 2:

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

ŷ = 27 + 15x₁ + 9x₂

The data used to develop the model came from a survey of 10 stores; for those data, SST = 19,000 and SSR = 14,820.

(a)

For the estimated regression equation given, compute

R².

R² =

(b)

Compute

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

Answer 1

part2 78% of variation in y variable is explained by independent variables.

From the value of R square we say that large amount of variation in dependent variable is explained by two independent variables.

As R square is 0.78

Means r is 0.8832 means there is high positive correlation between the dependent and independent variable.

And

Adjusted R square say that 75% of variability has been explained by the two independent variables.