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# 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
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.

##### Solution Summary

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

##### Solution Preview

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 ...

##### Measures of Central Tendency

Tests knowledge of the three main measures of central tendency, including some simple calculation questions.