An investor plans to develop a regression model for the appraisal value (in thou

Question

An investor plans to develop a regression model for the appraisal value (in thousands of dollars) of property in her city (Y) based on 5 numerical variables:

Y = 0 + 1X1 + 2X2 + 3X3 + 4X4 + 5X5 +

The investor would like to test whether or not the model has any significance. That is, she would like to test the hypotheses:

H0: 1 = 2 = 3 = 4 = 5 = 0

HA: not all j are zero

A sample of 30 items are drawn and the data is used to create the prediction equation:

y^ = b0 + b1x1 + b2x2 + b3x3 + b4x4 + b5x5

The regression sum of squares (SSR) is calculated to be 574.7 and the error sum of squares (SSE) is calculated to be 592.5. An F test is conducted to test the above hypotheses.

a)Calculate the test statistic (F) for this test. Give your answer to 2 decimal places.

F =

b)With a 99% level of confidence, the investor can or cannot reject the null hypothesis.

Explanation / Answer

a) Here,

Regression degrees of freedom = Number of independent variables = 5

Error degrees of freedom = 29 - 5 = 24

So,

F = (574.7 /5) / (592.5 /24)

F = 4.66

b) With a 99% level of confidence, the investor can reject the null hypothesis.

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