Question

Observations are taken on sales of a certain mountain bike in 22 sporting goods stores. The regression model was Y = total sales (thousands of dollars), X1 = display floor space (square meters), X2 = competitors' advertising expenditures (thousands of dollars), X3 = advertised price (dollars per unit).

(a)	Fill in the values in the table given here. (Negative values should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Round your t-values to 3 decimal places and p-values to 4 decimal places.)

   

Predictor	Coefficient	SE	tcalc	p-value
Intercept	1,285.3	357.1
FloorSpace	11.322	1.57
Competing Ads	-6.682	3.904
Price	-0.14123	0.08485

  

(b-1)

What is the critical value of Student's t in Appendix D for a two-tailed test at α = 0.01? (Round your answer to 3 decimal places.)

     

t-value =

(b-2)	Choose the correct option.
	Only CompetingAds differs significantly from zero. Only FloorSpace differs significantly from zero. Only Price differs significantly from zero.

Answer 1

Solution:

We are given that: Observations are taken on sales of a certain mountain bike in 22 sporting goods stores.

The regression model was

Y = total sales (thousands of dollars),

X₁ = display floor space (square meters),

X₂ = competitors' advertising expenditures (thousands of dollars),

X₃ = advertised price (dollars per unit).

Part a) Fill in the values in the table given here.

To find t_calc , we divide each Coefficient number by corresponding Standard Error (SE) value and to find P-value, we use Excel command:

and

P-value :

=T.DIST.2T( ABS(t_calc) , df)

where df = n - p - 1 = 22 - 3 - 1 = 18

Thus we get:

Predictor	Coefficient	SE		tcalc		p-value
Intercept	1285.3	357.1	=1285.3/357.1	3.599	=T.DIST.2T(ABS(3.599),18)	0.0021
FloorSpace	11.322	1.57	=11.322/1.57	7.211	=T.DIST.2T(ABS(7.211),18)	0.0000
Competing Ads	-6.682	3.904	=-6.682/3.904	-1.712	=T.DIST.2T(ABS(-1.712),18)	0.1042
Price	-0.14123	0.08485	=-0.14123/0.08485	-1.664	=T.DIST.2T(ABS(-1.664),18)	0.1133

Part b-1) What is the critical value of Student's t in Appendix D for a two-tailed test at α = 0.01?

t critical value = 2.878

( since this is two tailed test, t critical values are ( -2.878 , 2.878) )

Part b-2)

since p-value for Floor Space is 0.0000 < 0.01 level of significance, thus Floor Space is significantly different from 0.

Thus correct option is: Only FloorSpace differs significantly from zero