Using 19 observations on each variable, a computer program generated the followi

ID: 3367172 • Letter: U

Question

Using 19 observations on each variable, a computer program generated the following multiple regression model y 87.3+6.38x1-1.93x If the standard errors of the coefficients of the independent variables are, respectively, 3.36 and 0.75 can you conclude that the independent variable x1 is needed in the regression model? Let ?1 and ?2 denote the coefficients of the 2 variables in this model, and use a two-sided hypothesis test and significance level of 0.10 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: (Choose one) ? The value of the test statistio: (Round to at least two decimal places.) The two critical values at the 0.10 level of significance: (Round to at least two decimal places.) and Can you conclude that the independent variable Yes O No r1 is needed in the regression model? Clear Undo Help

Explanation / Answer

Solution

?1 is the regression coefficient corresponding to x1. Let the least square estimate of ?1 be represented by ?1cap. We are given:

?1cap = 6.38, SE(?1cap) = 3.36, ? = 0.1

Testing whether x1 is needed in the regression, is equivalent to testing if ?1 = 0.

All requisite results as stipulated in the question are presented below:

[Note: Entries in the last column are given for better understanding of the steps and answers.]

Null Hypothesis

H0: ?1 = 0

i.e., x1 is not needed

Alternative

H1: ?1 ? 0

i.e., x1 is needed

Type of test statistic

t-statistic

Value of test statistic

t = (?1cap – 0)/ SE(?1cap)

= 6.38/3.36

= 1.90

Two critical values

- 1.74, 1.74

Lower and upper 5% points of t-distribution with DF = 17 (n - 2)

Is x1 needed?

Yes

tcal > tcrit => H0 is rejected. => H1 is accepted.

DONE