A Regression Analysis Relating a Company's Sales, Their Advertising Expenditure

question 109

Essay

A regression analysis relating a company's sales, their advertising expenditure, price (per unit), and time (taken per unit production) resulted in the following output. $\begin{array} { l l l l l l } \text { Regression Statistics } & & & & \\\text { Multiple R } & 0.9895 & & & \\\text { R Square } & 0.9791 & & & \\\text { Adjusted R Square } & 0.9762 & & & \\\text { Standard Error } & 232.29 & & & & \\\\ANOVA\\& d f & \text { SS } & M S & F & \text { Signifcance F } \\\text { Regression } & 3 & 53184931.86 & 17728310.62 & 328.56 & 0.0000\\\\\\& &{\text { Sandard }} \\& \text { Coeffcients } & \text { Error } & t \text { Stat } & P \text {-Value } \\\text { Intercept } & 927.23 & 1229.86 & 0.75 & 0.4593 \\\text { Advertising }\left(\mathrm{x}_{1}\right) & 1.02 & 3.09 & 0.33 & 0.7450 \\\text { Price }\left(\mathrm{x}_{2}\right) & 15.61 & 5.62 & 2.78 & 0.0112 \\\text { Time }\left(\mathrm{x}_{3}\right) & 170.53 & 28.18 & 6.05 & 0.0000\end{array}$ ​
a.
Using α = .05, determine whether or not the regression model is significant. Fully explain how you arrived at your conclusion (give numerical reasoning) and what your answer indicates.
b.
At α = .05, determine which variables are significant and which are not. Explain how you arrived at your conclusion (give numerical reasoning).
c.
Fully explain the meaning of R Square, which is given in the above regression results. Be very specific and give numerical explanation.

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Definitions:

Monopolist

An individual or firm that is the sole provider of a particular product or service, possessing significant market power to determine prices and output levels.

Price Increase

The rise in the cost of goods or services over time, typically reflected in higher consumer prices.

Marginal Revenue

Marginal Revenue is the additional income earned from selling one more unit of a product or service, crucial for decision-making regarding production levels.

Average Total Cost

Firm’s total cost divided by its level of output.