slr with inferences a chemical analysis of diesel engine exhaust from environmental science technology in 1984 recorded mass and elemental carbon (both in milligrams per cm squared) as part of a study about carbon aerosols. assume we are interested in whether or not mass can used to predict elemental carbon. response: explanatory: does a linear regression model appear appropriate? partial output: coefficients: estimate std. error t value pr(>|t|) (intercept) 30.98933 5.04626 6.141 2.90e-06 mass 0.73660 0.03441 21.404 < 2e-16 --- residual standard error: 11.83 on 23 degrees of freedom multiple r-squared: 0.9522, adjusted r-squared: 0.9501 f-statistic: 458.2 on 1 and 23 df, p-value: < 2.2e-16 what is the estimated slope? interpret this value. give the equation of the least squares line. predict the value of the mean elemental carbon in the exhaust when the mass is 200. are you able to compute a residual for when mass is 200 using the predicted value you just computed? in the context of this regression, is it correct to say that 95.22% of the observed variation in mass is explained by the linear relationship between mass and elemental carbon? explain. part 2 problem1. using the carbon data , compute a 95% confidence interval for the mean carbon when mass is 150. then, compute a 95% prediction interval for an individual response (carbon value) when the mass is 150. assume the average mass is 170. coefficients: estimate std. error t value pr(>|t|) (intercept) 30.98933 5.04626 6.141 2.90e-06 mass 0.73660 0.03441 21.404 < 2e-16 --- residual standard error: 11.83 on 23 degrees of freedom multiple r-squared: 0.9522, adjusted r-squared: 0.9501 f-statistic: 458.2 on 1 and 23 df, p-value: < 2.2e-16 ci for mean response: prediction interval for individual response: if you computed similar confidence intervals at a mass value of 300, would the prediction interval still be wider than the confidence interval for the mean response? would the intervals associated with mass of 150 be narrower or wider than those associated with mass of 300? why? what is the value of the residual standard deviation? what does this value measure? set up appropriate hypotheses and test whether or not mass is a significant predictor for elemental carbon. null hypothesis: alternative hypothesis: (assumptions checked below) test statistic: p-value: dist. of test stat: conclusion: remember that some of the regression assumptions can only be checked after the regression has been fit. identify the plots below and discuss what they tell you about if the assumptions are met for the hypothesis test you just performed. finally, create a confidence interval for the population slope for predicting elemental carbon using mass in diesel engine exhaust. interpret your interval
