Question

The accompanying multiple regression model was developed to relate receipts​ (revenue) of Broadway plays to the number of paying​ attendants, the number of​ shows, and the average ticket price. A hypothesis test​ (at alphaequals​0.05) for the true coefficient of ​# Shows with Upper H 0​: beta Subscript Showsequals0 and Upper H Subscript Upper A​: beta Subscript Showsnot equals0 produced a​ p-value of 0.413 and the null hypothesis was not rejected. An investor accepts this analysis but claims that it demonstrates that it​ doesn't matter how many shows are playing on​ Broadway; receipts will be essentially the same. Explain why this interpretation is not a valid use of this regression model. Be specific.

Answer 1

The interpretation is incomplete, just states about one independent variable impact, ignores the other variables in the model.

Explanation:

Regression states the relationship between independent variable (x's) & dependent variable (y). Hypothesis states the statistical significance of their relationships.

Given case multiple regression : y = b0 + b1x1 + b2x2 + b2x3 , where y = broadway plays revenue , x1= no. of paying attendants, x2 = no. of shows, x3 = average ticket price.

Null Hypothesis H0: b2 = 0; Alternate Hypothesis H1: b2 ≠ 0, denote whether x2 i.e 'no. of shows' significantly affect y i.e 'broadway plays revenue'.

However, the multiple regression model ignores effect of all other independent variables (x's - x1, x2, x3) affecting dependent variable (y - broadway plays revenue)