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T- Test of a Multiple Regression Model

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Using 19 observations on each variable, a computer program generated the following multiple regression model:

y = 43.7 - 1.83x_1 - 4.25x_2

If the standard errors of the coefficients of the independent variables are, respectively, 1.24 and 2.04, can you conclude that the independent variable is needed in the regression model?

Let B1 and B2 denote the coefficients of the 2 variables in this model, and use a two-sided hypothesis test and significance level of 0.05 to determine your answer.
Carry your intermediate computations to at least three decimal places and round your answers as specified in the table.

Fill out the following:

Null hypothesis Ho:

Alternate hypothesis H1:

Type of test statistic (F, t, z, chi square) degrees of freedom

The value of the test statistic round to at least two decimal places

The two critical values at the 0.05 level of significance round to at least two decimal places

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Solution Preview

H0: b1 = 0

Ha: b1 <> 0

Type of test statistic: t with 17 degrees of ...

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Hypothesis Testing : T-test of Multiple Regression Model and Critical Values

T test of a multiple regression model
Using observations on each variable, a computer program generated the following multiple regression model:

If the standard errors of the coefficients of the independent variables are, respectively,
, , , , and ,
can you conclude that the independent variable is needed in the regression model?
Let denote the coefficients of the variables in this model, and use a two-sided hypothesis test and significance level of to determine your answer.
Carry your intermediate computations to at least three decimal places and round your answers as specified in the table.

The null hypothesis:

The alternative hypothesis:

The type of test statistic: t Degrees of freedom:

The value of the test statistic (Round to at least 2 decimal places):

The two critical values at the 0.05 level of significance (round to at least 2 decimal places):

Can you conclude that the independent variable x2 is needed in the regression model?

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