A Regression Was Performed on a Sample of 20 Observations $\hat { y }$

question 32

Essay

A regression was performed on a sample of 20 observations.Two independent variables were included in the analysis, x and z.The relationship between x and z is z = x².The following estimated equation was obtained. $\hat { y }$ = 23.72 + 12.61x + .798z
The standard errors for the coefficients are sb₁ = 4.85 and sb₂ = .21.For this model, SSR = 520.2 and SSE = 340.6.
a.
Estimate the value of y when x = 5.
b.
Compute the appropriate t ratios.
c.
Test for the significance of the coefficients at the 5% level. Which variable(s) is(are) significant?
d.
Compute the multiple coefficient of determination and the adjusted multiple coefficient of determination. Interpret the meaning of the multiple coefficient of determination.
e.
Test the significance of the relationship among the variables at the 5% level of significance.

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Definitions:

Depreciation Expense

The allocation of the cost of a tangible asset over its useful life, reflecting wear and tear or obsolescence.

Accounts Receivable

Amounts owed to a company by customers for goods or services that have been delivered or used but not yet paid for.

Prepaid Expenses

Expenses paid in advance for goods or services, which are recognized as assets until they are consumed or the term of use expires.

Bonds Issued

Long-term securities issued by corporations or governments to raise capital, with a promise to pay back with interest.