3. (5 points) An experiment was performed in Sweden in 1961-62 to assess the eff

Question

3. (5 points) An experiment was performed in Sweden in 1961-62 to assess the effect of speed limits on the motorway accident rate (Svensson, 1981). The experiment was conducted on 92 days in each year, matched so that day j in 1962 was comparable to day j in 1961, with j 1, 92. For each day, one of the two years was randomly assigned to have the speed limit in effect and enforced, and the other year was assigned to not have the speed limit in effect. The responses are counts of the number of accidents on each day in each year. The indicator variable, limit, takes the value 1 if the speed limit was in effect and zero otherwise. In addition, the indicator variable, year, takes the value 1 if it is 1962 and zero if it is 1961 (a) (2 points) Use the correct R output below to write a summary of statistical findings about whether there is any evidence that speed limit affects the number of motorway accidents (including at least the effect estimate with its confidence interval and hypothesis testing) fiti glm (y year day t limit, family poisson) summary (fiti) Coefficients Pr (>Iz Estimate Std. Error z value (Intercept) 3.0467406 0.0372985 81.685 2e-16 0.0702 0.0605503 0.0334364 1.811 year day 0.0024164 0.0005964 4.052 5.09e-05 07 limit 0.1749337 0.0355784 4.917 (Dispersion parameter for binomial family taken to be 1) Null deviance: 625.25 on 183 degrees of freedom Residual deviance: 569.25 on 180 degrees of freedom fit2 glmly year day limit, family quasipoisson) summary (fit 2) Coefficients Pr ltl) Estimate Std. Error t value (Intercept) 3.046741 0.067843 44.909 2e-16 0.060550 0.060818 0.996 0.32078 year 2.227 0.02716 day 0.002416 0.001085 limit 0.174934 0.064714 2.703 0.00753 (Dispersion parameter for binomial family taken to be 3.308492) Null deviance: 625.25 on 183 degrees of freedom Residual deviance: 569.25 on 180 degrees of freedom

Explanation / Answer

Part a)

We can create a hypothesis for beta (regression coefficient) equal to 0 vs beta not equal to 0.

In the first model where family is poisson, p value for limit is less than 0.05 also with the other model p value is less than 0.05. At 95% confidence level or 0.05 alpha level, limit is an important variable to predict the number of accident.

Part b)

Oul null hypothesis in this case is beta for limit and year is zero while the alternative hypothesis is beta for interaction term (limit and year) is not zero.

P value is .6822, hence we accept our null hypothesis that this interaction term has no effect in our model, we can remove this interaction term from our model.

Part c)

In our study blocking variable is year becuase it is the least significant variable. We can see P value to check for Variable of importance, P value is more than .05.

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