# Regression Analysis Interpretations

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1) Blay mount Amateur Dramatic Society is staging a play and wants to know how much to spend on advertising, by getting a better understanding of the relationship between advertising and attendance. For the past 11 productions they have recorded their spending on advertising (in $) and the size of their audience and have performed a regression of attendance on spending (the resulting regression output is below). Unfortunately, none of the society members has taken a statistics (or Quantitative Analysis) course. To explain these regression results to the society, specifically address the following:

a) the overall statistical significance of the regression

b) the interpretation and the statistical significance of the intercept term

c) the statistical significance of the spending variables (with such a small data set you decide to use a significance level of 10% to determine statistical significance)

d) the relationship between advertising expenditures and attendance

i. If they were already planning to spend $500 on advertising for their next production, what would happen to attendance if they decided to spend a dollar more (i.e., the marginal benefit of advertising)? Round to the nearest whole person!

ii. If instead they were planning to spend only $100 on advertising for the upcoming production, what would happen to attendance if they decided to spend a dollar more? Round to the nearest whole person!

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.931647116

R Square 0.867966348

Adjusted R Square 0.834957935

Standard Error 88.75504356

Observations 11

ANOVA

df SS MS F Significance F

Regression 2 414280.3379 207140.2 26.29531 0.000303905

Residual 8 63019.66205 7877.458

Total 10 477300

Coefficients Standard Error t Stat P-value

Intercept -190.171507 113.6546959 -1.67324 0.132817

Spending (in $) 2.357834083 0.649257794 3.631584 0.00667

Spending Squared -0.00175563 0.000811289 -2.164 0.0624.

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##### Solution Summary

Regression analysis interpretations are examined in the solution. The relationship between advertising expenditures and attendances are determined.

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See the attached file.

1) Blay mount Amateur Dramatic Society is staging a play and wants to know how much to spend on advertising, by getting a better understanding of the relationship between advertising and attendance. For the past 11 productions they have recorded their spending on advertising (in $) and the size of their audience and have performed a regression of attendance on spending (the resulting regression output is below). Unfortunately, none of the society members has taken a statistics (or Quantitative Analysis) course. To explain these regression results to the society, specifically address the following:

a) the overall statistical significance of the regression

b) the interpretation and the statistical significance of the intercept term

c) the statistical significance of the spending variables (with such a small data set you decide to use a significance level of 10% to determine statistical significance)

d) the relationship between advertising expenditures and attendance

i. If they were already planning to spend $500 on advertising for their next production, what would happen to attendance if they decided ...

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