The demand model relating the quantity of good XYZ sold QXYZ

The demand model relating the quantity of good XYZ sold (QXYZ) to the price of good (PXYZ) is reported below:

QXYZ = 4.46 + .304 PXYZ

Coefficient      Standard Error

4.46                 3.04

.304                 .3243

Analysis of Variance:

Source             DF                   Sum of Squares

Regression                                   141.9

Residual                                   3718.9

Total                24

Refer to this scenario What is the t-statistic for the slope coefficient?

3.04

0.94

0.30

4.46

Refer to the previous scenario, is the slope coefficient statistically different from zero?

Yes

No

Inconclusive

None of the above

Solution

QXYZ = 4.46 + 0.304 PXYZ

slope coeffcient=0.304

standard error of slope coefficient (SE) =0.3243

t statistic=slope coefficient/SE

              =0.304/0.3243

               =0.94

Null hpothesis: slope coefficient is 0

Let level of significance be 5% (two table)

From anova table, degress of freedom of total sum of squares=24=n-1;where n is no of observations

n-1=24

From t table, critical value of t at 5% significance and 24 degrees of freedom is 2.064

Since t calculated(0.94)<t critical(2.064)

We do not reject null hypothesis

So slope coefficient is not statistically different from 0.

Answer is NO.