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 2 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 ...
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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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