ABC relates the speed, Y $,$ with which a particular insurance motivation is adopted to the size of the insurance firm and the type of the firm. The dependent variable is measured by the number of months elapsed between the time the first firm adopted the innovation and the time the firm being considered adopted the innovation. The size of the insurance firm, X $1,$ is measured by the total assets of the firm, and the type of the firm, X $2,-$ a qualitative "dummy" independent variable $-$ is either a mutual company or a stock company. The data in the following table are observed:

Hint: Note that you first have to code Type of Firm as $0$ or $1.$

Firm

Number of Months Elapsed $($Y$)$

Size of Firm $($$ millions$)$

Type of Firm

$1$

$17$

$151$

Mutual

$2$

$26$

$92$

Mutual

$3$

$21$

$175$

Mutual

$4$

$30$

$31$

Mutual

$5$

$22$

$104$

Mutual

$6$

$0$

$277$

Mutual

$7$

$12$

$210$

Mutual

$8$

$19$

$120$

Mutual

$9$

$4$

$290$

Mutual

$10$

$16$

$238$

Mutual

$11$

$28$

$164$

Stock

$12$

$15$

$272$

Stock

$13$

$11$

$295$

Stock

$14$

$38$

$68$

Stock

$15$

$31$

$85$

Stock

$16$

$21$

$224$

Stock

$17$

$20$

$166$

Stock

$18$

$13$

$305$

Stock

Are there any multicollinearity issues? Discuss.

Determine the regression equation that is used to predict speed $($the number of months elapsed$)$ based only on the size of the firm.

How much of the variation in speed is explained by the size of the firm only?

Determine the regression equation$($s$)$ that is used to predict speed $($the number of months elapsed$)$ based on the size of the firm and the type of the firm. Interpret the practical meaning of $2.$

What is the value of R $2($in the case of the multiple regression$)?$ How can we interpret it$?$ What is the unexplained variation?

What is the change in R $2$ in the two regressions that you ran? Comment on it$.$

Is the model significant? Make sure you state the null and alternative hypotheses. Use alpha $=0\mathrm{.}05.$

Are the regression coefficients significant? Explain. Make sure you state the null and alternative hypotheses. Use alpha $=0\mathrm{.}05.$ Would you consider deleting any of the variables? Explain.