A pharmaceutical company is debating introducing a new sleeping pill that helps patients with sleep related disorders (like insomnia) fall asleep fast and sleep sounder. They plan on posting an advert on a social networking site to check how many "Likes" they get. Their conjecture is: older people are more likely to welcome the drug compared to younger ones and a small pilot survey of 80 people (randomly chosen) generated the attached R output Of interest are the variables "age" (in years) and is a nan-negative variable that describes how strongly a person is willing to hit the "Like" button. Higher the score, stronger the urge] The R output is on the next page. O. 04701 O a 001 a. Write out the fitted (i=e the estimated) model that connects a person's to his/her age (in years). b. how much isa person's expected to change due toa one-month increase in his/her age? c. What proportion of variation in is explained by this model? d. (I p!) Find the simple correlation coefficient between these two variables. e. To check whether "age" is a significant predictor in this context: Write out the null and the alternate hypotheses. Find the value of the test statistic and the p-value Hence, reach a decision at = 0.05. From the R output, I found that the point estimate for the slope I) is 0129. Since this is verv close to O, I decided to fall to reject the null and claim that "age" is not a significant predictor. Am I right? Please justify. Check the same claim through a 95% confidence interval for the slope parameter. What is the margin of error of this interval? f. John just had his 60-th birthday. Estimate his both a point estimate (i.e., a single number) a 95% prediction interval. g. Are you making any assumptions on part (f)? h. Recall that a perfect regression world, the residuals from a fit are expected to follow a normal distribution. In our case, with mean O and variance 8.6. The pharmaceutical company believes the fit in question S is bad if among the first three residuals, the first one is the second one is at most -2.93, and the third one is at least 8_79. Find the probability that the fit is bad. You may assbme independence among the residuals.