Please show the work below:

2. in a study of innovation in the insurance industry. an economist wishes to relate the speed with which a particular insurance innovation is adopted [y] to the size of the insurance nn [x1] and the type of Fun. The response variable is measured by the number of months elapsed between the time the rst rm adopted the innovation and the time the given rm adopted the innovation. The size of rm is measured by the amount of total assets of the rm. The type of rm is a categorical variable composed of two levelsstock companies and mutual companies. do indicator is dened to represent this variable: x; = 1 if stock company and = i] if mutual company. Then. a linear model. y = , + 3111 + .8312 + axlxz + E. is tted to the sample data. The R output is given below. Coefficients: Estimate Std. Error t value Prleltil lInterceptl 33.0363695 2.4406490 13.064 2.4?2-10 '** :1 -0.1015306 0.0130525 -T.T?5 7.91e-07 *'* :2 3.1312501 3.554051? 2.225 0.0400 * xltxz -0.0004111 0.0183312 -0.023 0-9321 Signif. codes: 0 \"*" 0.001 '*" 0.01 \"' 0.05 '.' 0.1 ' ' 1 Residual standard error: 3.32 on 16 degrees of freedom Multiple R-nquared: 0.3961, Adjusted R-oquared: 0.6154 r-Itatiltict 45.49 on 3 and 16 BF. p-velue: 4.675e-06 [A] [3 points} How many rms are included in the study? Explain. [B] [6 points} Interpret the coefcients h... hi. ha, and ha in the context of the problem [C] [B po nts Using rt = 0.05. test whether the interaction term can be dropped. State the hypotheses, the value of test statistic. p-value. and your conclusion. [D] [5 points} Based on the output. is it able to test whether both 1:2 and xix; can be dropped simultaneously using or = 0.01? "so, perform the test: otherwise. explain. [E] [4 points] if the type ol'rm were composed of k levels [it :e 2], how would you include this categorical variable in the regression model