Question
In: Statistics and Probability
The accompanying table provides data for tar, nicotine, and carbon monoxide (CO) contents in a certain...
The accompanying table provides data for tar, nicotine, and carbon monoxide (CO) contents in a certain brand of cigarette. Find the best regression equation for predicting the amount of nicotine in a cigarette. Why is it best? Is the best regression equation a good regression equation for predicting the nicotine content? Why or why not?
Tar Nicotine CO
5 0.5 5
17 1.0 19
16 1.1 18
13 0.7 19
13 0.8 18
15 1.1 13
15 1.0 17
16 1.2 16
15 1.1 15
9 0.7 11
13 0.8 17
12 0.8 17
14 0.7 17
16 1.1 16
3 0.3 3
14 1.0 18
15 1.1 16
13 0.7 19
15 1.0 16
15 1.0 17
16 1.2 15
15 1.1 16
7 0.7 7
17 1.3 15
15 1.0 14
Find the best regression equation for predicting the amount of nicotine in a cigarette. Use predictor variables of tar and/or carbon monoxide (CO). Select the correct choice and fill in the answer boxes to complete your choice.
A. Nicotine = __ + (__) CO
B. Nicotine = __ + (__) Tar
C. Nicotine = __ + (__) Tar + (__) CO
Solutions
Expert Solution
A.
| X - Mx | Y - My | (X - Mx)2 | (X - Mx)(Y - My) |
| -9.96 | -0.42 | 99.2016 | 4.1832 |
| 4.04 | 0.08 | 16.3216 | 0.3232 |
| 3.04 | 0.18 | 9.2416 | 0.5472 |
| 4.04 | -0.22 | 16.3216 | -0.8888 |
| 3.04 | -0.12 | 9.2416 | -0.3648 |
| -1.96 | 0.18 | 3.8416 | -0.3528 |
| 2.04 | 0.08 | 4.1616 | 0.1632 |
| 1.04 | 0.28 | 1.0816 | 0.2912 |
| 0.04 | 0.18 | 0.0016 | 0.0072 |
| -3.96 | -0.22 | 15.6816 | 0.8712 |
| 2.04 | -0.12 | 4.1616 | -0.2448 |
| 2.04 | -0.12 | 4.1616 | -0.2448 |
| 2.04 | -0.22 | 4.1616 | -0.4488 |
| 1.04 | 0.18 | 1.0816 | 0.1872 |
| -11.96 | -0.62 | 143.0416 | 7.4152 |
| 3.04 | 0.08 | 9.2416 | 0.2432 |
| 1.04 | 0.18 | 1.0816 | 0.1872 |
| 4.04 | -0.22 | 16.3216 | -0.8888 |
| 1.04 | 0.08 | 1.0816 | 0.0832 |
| 2.04 | 0.08 | 4.1616 | 0.1632 |
| 0.04 | 0.28 | 0.0016 | 0.0112 |
| 1.04 | 0.18 | 1.0816 | 0.1872 |
| -7.96 | -0.22 | 63.3616 | 1.7512 |
| 0.04 | 0.38 | 0.0016 | 0.0152 |
| -0.96 | 0.08 | 0.9216 | -0.0768 |
| SS: 428.96 | SP: 13.12 |
Sum of X = 374
Sum of Y = 23
Mean X = 14.96
Mean Y = 0.92
Sum of squares (SSX) = 428.96
Sum of products (SP) = 13.12
Regression Equation = ŷ = bX + a
b = SP/SSX = 13.12/428.96 =
0.0306
a = MY - bMX = 0.92 -
(0.03*14.96) = 0.4624
ŷ = 0.0306X + 0.4624
B.
| X - Mx | Y - My | (X - Mx)2 | (X - Mx)(Y - My) |
| -8.36 | -0.42 | 69.8896 | 3.5112 |
| 3.64 | 0.08 | 13.2496 | 0.2912 |
| 2.64 | 0.18 | 6.9696 | 0.4752 |
| -0.36 | -0.22 | 0.1296 | 0.0792 |
| -0.36 | -0.12 | 0.1296 | 0.0432 |
| 1.64 | 0.18 | 2.6896 | 0.2952 |
| 1.64 | 0.08 | 2.6896 | 0.1312 |
| 2.64 | 0.28 | 6.9696 | 0.7392 |
| 1.64 | 0.18 | 2.6896 | 0.2952 |
| -4.36 | -0.22 | 19.0096 | 0.9592 |
| -0.36 | -0.12 | 0.1296 | 0.0432 |
| -1.36 | -0.12 | 1.8496 | 0.1632 |
| 0.64 | -0.22 | 0.4096 | -0.1408 |
| 2.64 | 0.18 | 6.9696 | 0.4752 |
| -10.36 | -0.62 | 107.3296 | 6.4232 |
| 0.64 | 0.08 | 0.4096 | 0.0512 |
| 1.64 | 0.18 | 2.6896 | 0.2952 |
| -0.36 | -0.22 | 0.1296 | 0.0792 |
| 1.64 | 0.08 | 2.6896 | 0.1312 |
| 1.64 | 0.08 | 2.6896 | 0.1312 |
| 2.64 | 0.28 | 6.9696 | 0.7392 |
| 1.64 | 0.18 | 2.6896 | 0.2952 |
| -6.36 | -0.22 | 40.4496 | 1.3992 |
| 3.64 | 0.38 | 13.2496 | 1.3832 |
| 1.64 | 0.08 | 2.6896 | 0.1312 |
| SS: 315.76 | SP: 18.42 |
Sum of X = 334
Sum of Y = 23
Mean X = 13.36
Mean Y = 0.92
Sum of squares (SSX) = 315.76
Sum of products (SP) = 18.42
Regression Equation = ŷ = bX + a
b = SP/SSX = 18.42/315.76 =
0.0583
a = MY - bMX = 0.92 -
(0.06*13.36) = 0.1406
ŷ = 0.0583X + 0.1406
C.
| X1-Mx1 | X2-Mx2 | Y-My | (X1-Mx1)2 | (X2-Mx2)2 | SPx1y | SPx2y | SPx1x2 |
| -9.96 | -8.36 | -0.42 | 99.202 | 69.89 | 4.183 | 3.511 | 83.266 |
| 4.04 | 3.64 | 0.08 | 16.322 | 13.25 | 0.323 | 0.291 | 14.706 |
| 3.04 | 2.64 | 0.18 | 9.242 | 6.97 | 0.547 | 0.475 | 8.026 |
| 4.04 | -0.36 | -0.22 | 16.322 | 0.13 | -0.889 | 0.079 | -1.454 |
| 3.04 | -0.36 | -0.12 | 9.242 | 0.13 | -0.365 | 0.043 | -1.094 |
| -1.96 | 1.64 | 0.18 | 3.842 | 2.69 | -0.353 | 0.295 | -3.214 |
| 2.04 | 1.64 | 0.08 | 4.162 | 2.69 | 0.163 | 0.131 | 3.346 |
| 1.04 | 2.64 | 0.28 | 1.082 | 6.97 | 0.291 | 0.739 | 2.746 |
| 0.04 | 1.64 | 0.18 | 0.002 | 2.69 | 0.007 | 0.295 | 0.066 |
| -3.96 | -4.36 | -0.22 | 15.682 | 19.01 | 0.871 | 0.959 | 17.266 |
| 2.04 | -0.36 | -0.12 | 4.162 | 0.13 | -0.245 | 0.043 | -0.734 |
| 2.04 | -1.36 | -0.12 | 4.162 | 1.85 | -0.245 | 0.163 | -2.774 |
| 2.04 | 0.64 | -0.22 | 4.162 | 0.41 | -0.449 | -0.141 | 1.306 |
| 1.04 | 2.64 | 0.18 | 1.082 | 6.97 | 0.187 | 0.475 | 2.746 |
| -11.96 | -10.36 | -0.62 | 143.042 | 107.33 | 7.415 | 6.423 | 123.906 |
| 3.04 | 0.64 | 0.08 | 9.242 | 0.41 | 0.243 | 0.051 | 1.946 |
| 1.04 | 1.64 | 0.18 | 1.082 | 2.69 | 0.187 | 0.295 | 1.706 |
| 4.04 | -0.36 | -0.22 | 16.322 | 0.13 | -0.889 | 0.079 | -1.454 |
| 1.04 | 1.64 | 0.08 | 1.082 | 2.69 | 0.083 | 0.131 | 1.706 |
| 2.04 | 1.64 | 0.08 | 4.162 | 2.69 | 0.163 | 0.131 | 3.346 |
| 0.04 | 2.64 | 0.28 | 0.002 | 6.97 | 0.011 | 0.739 | 0.106 |
| 1.04 | 1.64 | 0.18 | 1.082 | 2.69 | 0.187 | 0.295 | 1.706 |
| -7.96 | -6.36 | -0.22 | 63.362 | 40.45 | 1.751 | 1.399 | 50.626 |
| 0.04 | 3.64 | 0.38 | 0.002 | 13.25 | 0.015 | 1.383 | 0.146 |
| -0.96 | 1.64 | 0.08 | 0.922 | 2.69 | -0.077 | 0.131 | -1.574 |
| SSX1: 428.96 | SSX2: 315.76 | SPX1Y: 13.12 | SPX2Y: 18.42 | SPX1X2: 306.36 |
Sum of X1 = 374
Sum of X2 = 334
Sum of Y = 23
Mean X1 = 14.96
Mean X2 = 13.36
Mean Y = 0.92
Sum of squares (SSX1) = 428.96
Sum of squares (SSX2) = 315.76
Sum of products (SPX1Y) = 13.12
Sum of products (SPX2Y) = 18.42
Sum of products (SPX1X2) = 306.36
Regression Equation = ŷ = b1X1 +
b2X2 + a
b1 =
((SPX1Y)*(SSX2)-(SPX1X2)*(SPX2Y))
/
((SSX1)*(SSX2)-(SPX1X2)*(SPX1X2))
= -1500.38/41591.96 = -0.0361
b2 =
((SPX2Y)*(SSX1)-(SPX1X2)*(SPX1Y))
/
((SSX1)*(SSX2)-(SPX1X2)*(SPX1X2))
= 3882/41591.96 = 0.0933
a = MY - b1MX1 -
b2MX2 = 0.92 - (-0.04*14.96) -
(0.09*13.36) = 0.2127
ŷ = -0.0361X1 + 0.0933X2 +
0.2127
orchestra answered 3 years agoRelated Solutions
The accompanying table provides data for tar, nicotine, and carbon monoxide (CO) contents in a certain...
The accompanying table provides data for tar, nicotine, and
carbon monoxide (CO) contents in a certain brand of cigarette.
Find the best regression equation for predicting the amount of
nicotine in a cigarette. Why is it best? Is the best regression
equation a good regression equation for predicting the nicotine
content? Why or why not?
TAR
NICOTINE
CO
6
0.4
5
15
1.0
18
16
1.3
16
13
0.7
18
13
0.8
18
13
0.9
14
16
1.0
17
16...
The accompanying table provides data for tar, nicotine, and carbon monoxide (CO) contents in a certain...
The accompanying table provides data for tar, nicotine, and
carbon monoxide (CO) contents in a certain brand of cigarette.
Find the best regression equation for predicting the amount of
nicotine in a cigarette. Why is it best? Is the best regression
equation a good regression equation for predicting the nicotine
content? Why or why not?
Tar Nicotine CO
5 0.5 3
15 1.0 19
17 1.1 16
14 0.7 19
14 0.8 19
14 1.0 13
15 1.0 16
14 ...
The accompanying table, MultiLinear Regression 5, provides data for tar, nicotine, and carbon monoxide (CO) contents...
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
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