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F test of a multiple regression model.

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A company that manufactures computer chips wants to use a multiple regression model to study the effect that 4 different variables have on y, the total daily production cost (in thousands of dollars). Let denote the coefficients of the 4 variables in this model. Using 19 observations on each of the variables, the software program used to find the estimated regression model reports that the total sum of squares (SST) is 661.86 and the regression sum of squares (SSR) is 159.36 . Using a significance level of .10, can you conclude that at least one of the independent variables in the model provides useful (i.e., statistically significant) information for predicting daily production costs?

Perform a one-tailed test. Then fill in the table below.

The null hypothesis
The alternative hypothesis
The type of test statistic
The value of the test statistic (round to two decimal places)
The critical value at .10 level of significance.

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Null Hypothesis:
H0: b1 = b2 = ... = bp = 0
(No linear relationships)

Alternative Hypothesis
H1: At least one bi != 0 (beta i not equal ...

Solution Summary

This solution uses hypothesis testing at an alpha of .10 to prove whether or not an independent variable has a statistically significant impact on the dependent variable.

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F test of a multiple regression model

F test of a multiple regression model
To help schedule staffing and equipment needs, a large hospital uses a multiple regression model to predict its 'bed census' , the number of beds occupied at the end of each day. Using hospital records from the most recent days, a total of independent variables are used to find the estimated regression model. Let and denote the coefficients of the variables in this model. A computer printout indicates that the total sum of squares (SST) associated with the model is and the corresponding regression sum of squares (SSR) is . Using a significance level of , can you conclude that at least one of the independent variables in the model provides useful (i.e., statistically significant) information for predicting daily bed census?
Perform a one-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places and round your answers as specified in the table.

Ho:
H1:at least one of the independent variables is useful
The type of test statistic (chi square, t, F, z) degrees of freedom__
The value of the test statistic (round to at least two decimal places)___
The p-value (round to at least two decimal places)___

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