You work at a large roller skating rink: Rink-A-Dink. You are asked to use regre

Question

You work at a large roller skating rink: Rink-A-Dink. You are asked to use regression analysis to estimate the relationship between skate rentals and customer ages. These are your results:

a) How many observations are included in this analysis?

b) What is the coefficient of determination and what does it tell us?

c) What does the parameter estimate on age tell us?

d) What is the corresponding t-statistic for the age variable? Is it significant according to the corresponding P-value? If so, at which critical value/confidence level?

e) Is the F-statistic significant according to the corresponding P-value? If so, at which critical value/confidence level? What does this mean?  

P-Value on Dependent Variable: Skates Observations: 125 R-Square F-Ratio 18.82 0.8154 0.005914 Parameter Standard Variable Estimate Error T-RatioP-Value (intercept) 52.3 4.18 12.49 0.86 0.0068 0.0125 8.26

Explanation / Answer

a) Number of observations are 125

b) The coefficient of determination is the value of R-square = 0.8154. It tells us that 81.54% of variation in skates is explained by the iexplanatory variable age.

c) It tells us that if the age increases by one year on an average skate rentals increases by 8.26 dollars.

d) t-ratio = 8.26/0.86 = 9.604. Yes it is significant because the p-value is very small close to zero.

e) Yes, it is significant at 1% level of significance. It means that age variable explains the changes in sakte rentals.

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