Question

The accompanying table, MultiLinear Regression 5, provides data for tar, nicotine, and carbon monoxide (CO) contents in a certain brand of cigarette. All measurements are in milligrams (mg).

MultiLinear Regression 5

Nicotine (Y)	Tar (X1)	CO (X2)
0.4	5	3
0.9	9	11
0.7	12	18
0.8	13	18
1	16	18
0.6	6	6
0.9	15	18
1.1	15	15
0.8	13	18
1.2	17	16

Part a) Run the Multilinear Regression Analysis in Excel with both predictor variables. What is the adjusted R² value to the nearest hundredth of a percent (i.e. 45.67%)?
Adjusted R² =

Part b) What is the p-value for the full model? Round answer to nearest thousandth of a percent (i.e. 0.123%).
Model p-value =

Part c) What are the p-values for the variable coefficients? Round answers to the nearest hundredth of a percent (i.e. 0.12%)
Tar p-value =

CO p-value =

Part d) Run simple linear regression for just Nicotine & Tar and then for just Nicotine & CO. Write down the R²
values and p-values for those two models.

Model	R2 value (hundredth percent, i.e. 12.34%)	Model p-value (thousandth percent, i.e. 0.123%)
Nicotine & Tar
Nicotine & CO

Part e) Using your analyses from parts a) through d), determine the model that is the best fit for these data. Use a significance level of 0.05, and consider each model’s p-value, R² value (or adjusted R² value), the p-values for each of the coefficients to determine the best fit model. Use that model to estimate the Nicotine level in a cigarette having 9 mg of tar and 9 mg of CO. Round answer to nearest hundredth of a milligram (i.e. 0.81 mg).
Predicted Nicotine Level =

Answer 1

Please find Excel Output attached in image

a.)

Adjusted R² = 76.99%

b.)

p-value for Full Model;

p = 0.00242 = 0.242%

c.) p-value for individual coefficients

For Tar (X1), p = 0.00501 = 0.501%

For CO (X2), p = 0.1431 = 14.31%

d.)

For Nicotine and Tar:

For Nicotine and CO:

Model	Adjusted R-square	P-value
Nic and tar	72.05%	0.11%
Nic and CO	33.24%	4.73%

e.)

Based on Adjusted R-square and model p-Value, first model looks best, Although variable CO(X2) p-value shows that its insignificant and can be removed

So, For CO(X2) = 9 and Tar (X1) = 9   

Predicted Nicotin = 0.71 mg