Question

The regression equation NetIncome = 2,159 + .0312 Revenue was estimated from a sample of 100 leading world companies (variables are in millions of dollars).

(a-1) Calculate the residual for the x, y pair ($45,533, $2,697). (A negative value should be indicated by a minus sign. Round your answer to 4 decimal places.) Residual
(a-2) Did the regression equation underestimate or overestimate the net income? The regression equation overestimated the net income. The regression equation underestimated the net income.
(b-1) Calculate the residual for the x, y pair ($60,417, $3,497). (A negative value should be indicated by a minus sign. Round your answer to 4 decimal places.) Residual
(b-2) Did the regression equation underestimate or overestimate the net income? The regression equation overestimated the net income. The regression equation underestimated the net income.

Answer 1

a) -882.6296

b) The regression equation overestimated the net income.

c) -547.0104

d) The regression equation overestimated the net income.

Explanation:

We are given the following information in the question:

The regression equation for net income is given by:

`\text{Net Income} = y = 2159 + .0312(\text{Revenue})`

a) residual for the (x, y) pair ($45,533, $2,697)

Calculated net income =

`2159 + .0312(45533) = 3579.6296`

Residual = Observed net income - Calculated net income

`\text{Residual} = 2697-3579.6296 = -882.6296`

b) The regression equation overestimated the net income.

c) residual for the (x, y) pair ($60,417, $3,497)

Calculated net income =

`2159 + .0312(60417) = 4044.0104`

Residual = Observed net income - Calculated net income

`\text{Residual} = 3497-4044.0104 = -547.0104`

d) The regression equation overestimated the net income.