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 alphaequals0.05) 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.

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)