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

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.