If the coefficient 1 has a nonzerovalue, then it is helpful in predicting the value of the response variable. If 1=0, it is not helpful in predicting the value of the response variable and can be eliminated from the regression equation. To test the claim that 1=0 use the test statistic t=b10/sb. Critical values orP-values can be found using the t distribution with n(k+1) degrees offreedom, where k is the number of predictor(x) variables and n is the number of observations in the sample. The standard error sb1 is often provided by software. Forexample, see the accompanying technologydisplay, which shows that sb1=0.074400996 (found in the column with the heading of"Std. Err." and the row corresponding to the first predictor variable ofheight). Use the technology display to test the claim that 1=0. Also test the claim that 2=0. What do the results imply about the regressionequation?

Parameter estimates:

Parameter

Estimate

Std. Err.

Alternative

DF

T-Stat

P-value

Intercept

149.84358

12.568581

0

150

11.922076

<0.0001

Height

0.77603374

0.074400996

0

150

10.430421

<0.0001

Waist

1.0315006

0.033364065

0

150

30.916515

<0.0001

For H0: beta 1 greater than 0 comma

1>0,

beta 1 less than 0 comma

1<0,

beta 1 not equals 0 comma

10,

beta 1 equals 0 comma

1=0,

the test statistic is t=

and theP-value is

, so

do not reject

reject

H0 and conclude that the regression coefficient b1=

should

not be

be

kept.

(Round to three decimal places asneeded.)

Test the claim that 2=0.

For H0: beta 2 greater than 0 comma

2>0,

beta 2 equals 0 comma

2=0,

beta 2 not equals 0 comma

20,

beta 2 less than 0 comma

2<0,

the test statistic is t=

and theP-value is

, so

reject

do not reject

H0 and conclude that the regression coefficient b2=

nothing

should

not be

be

kept.

(Round to three decimal places asneeded.)

What do the results imply about the regressionequation?

A.

The results imply that the regression equation should not include either independent variable since both height and waist will not be useful in predicting the response variable.

B.

The results imply that the regression equation should only include the independent variable of height since waist will not be useful in predicting the response variable.

C.

The results imply that the regression equation should include both independent variables of height and waist as both are useful in predicting the response variable.

D.

The results imply that the regression equation should only include the independent variable of waist since height will not be useful in predicting the response variable.