Question
In: Statistics and Probability
Observations are taken on sales of a certain mountain bike in 22 sporting goods stores. The...
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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. | ||||||
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Solutions
Expert Solution
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 tcalc , 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(tcalc) , 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
orchestra answered 2 years agoRelated Solutions
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