Question

Brand   Tar   Nicotine   CO
American_Filter   16   1.2   15
Benson_&_Hedges   16   1.2   15
Camel   16   1   17
Capri   9   0.8   6
Carlton   1   0.1   1
Cartier_Vendome   8   0.8   8
Chelsea   10   0.8   10
GPC_Approved   16   1   17
Hi-Lite   14   1   13
Kent   13   1   13
Lucky_Strike   13   1.1   13
Malibu   15   1.2   15
Marlboro   16   1.2   15
Merit   9   0.7   11
Newport_Stripe   11   0.9   15
Now   2   0.2   3
Old_Gold   18   1.4   18
Pall_Mall   15   1.2   15
Players   13   1.1   12
Raleigh   15   1   16
Richland   17   1.3   16
Rite   9   0.8   10
Silva_Thins   12   1   10
Tareyton   14   1   17
Triumph   5   0.5   7
True   6   0.6   7
Vantage   8   0.7   11
Viceroy   18   1.4   15
Winston   16   1.1   18

a) Find the regression equation that expresses the response variable​ (y) of nicotine amount in terms of the predictor variable​ (x) of the tar amount.

​b) Find the regression equation that expresses the response variable​ (y) of nicotine amount in terms of the predictor variable​ (x) of the carbon monoxide amount.

​c) Find the regression equation that expresses the response variable​ (y) of nicotine amount in terms of predictor variables​ (x) of tar amount and carbon monoxide amount.

​d) For the regression equations found in parts​ (a), (b), and​ (c), which is the best equation for predicting the nicotine​ amount? Justify your answer.

​e) Is the best regression equation identified in part​ (d) a good equation for predicting the nicotine​ amount? Why or why​ not?

Answer 1

a) Here the response variable is nicotine amount (y) and predictor is tar amount (x). The regression equation is given by

   y = 0.154030 + 0.065052*x

b) Here the response variable is nicotine amount (y) and predictor is carbon monoxide amount (x). The regression equation is given by

y= 0.191639 + 0.060564*x

c) Here the response variable is nicotine amount (y) and predictors are tar amount (x1) and carbon monoxide amount (x2). The regression equation is given by

y= 0.181645 + 0.081837*x1 - 0.018642*x2

d) The best equation for predicting niocotine amount is the equation in part(c) as the value of multiple correlation coefficient is 0.9333 which is highest among the 3 regressions.

e) The best regression equation identified in part (d) may not always be a good choice for predicting nicotine amount since the predictors ie. tar amount and carbon monoxide amount are highly correlated ie. multicollinearity is present in the data set.

The R code is attached.