1. Using data set HW3_SM.txt, build a multiple linear regression model between Y
ID: 3366583 • Letter: 1
Question
1. Using data set HW3_SM.txt, build a multiple linear regression model between Y and (X1,X2,X3,X4).
(a) Based on the estimate for parameters and their standard errors, construct a 95% confidence interval for
Beta2.
Data set from HW3_SM.txt below
Y X1 X2 X3 X4
19.55 1.68 0.89 0.61 1.69
20.63 1.11 0.66 0.41 1.64
24.16 1.63 1.02 0.63 1.66
14.82 1.94 0.29 0.14 1.44
16.43 2.18 0.75 0.42 1.38
19.56 1.77 0.53 0.56 1.61
20.35 2.66 0.76 0.48 1.42
18.3 1.75 0.71 0.47 1.31
20.48 1.65 1.08 0.4 1.36
25.11 1.6 0.95 0.36 1.61
19.15 1.95 0.28 0.62 1.69
24.16 2.24 0.81 0.43 1.73
20.27 2.34 0.77 0.34 1.46
18.74 2.67 0.39 0.53 1.38
23.06 1.86 0.97 0.51 1.55
26.25 1.66 1.17 0.48 1.56
20.01 2.27 0.51 0.35 1.59
22.76 2.23 1.06 0.57 1.54
19.75 2.27 0.81 0.46 1.35
21.39 1.59 0.97 0.65 1.68
17.39 1.66 0.76 0.5 1.39
22.81 1.99 1.06 0.52 1.5
22.52 1.67 1.02 0.66 1.54
20.67 1.73 0.57 0.51 1.63
20.03 2.17 0.76 0.53 1.55
18 2.44 0.78 0.53 1.63
19.23 2.1 0.63 0.55 1.41
22.07 1.57 1.19 0.4 1.4
19.82 1.81 0.9 0.46 1.46
20.3 2.38 0.93 0.4 1.31
18.58 2.41 0.51 0.71 1.62
17.72 1.72 1.02 0.31 1.48
19.5 1.84 1.07 0.48 1.49
15.72 1.78 0.68 0.7 1.29
20.34 2.24 0.76 0.45 1.66
22.43 1.64 0.71 0.36 1.45
23.57 2.37 0.86 0.54 1.58
23.31 2.04 1.04 0.51 1.45
21.25 2.03 0.95 0.59 1.41
18.23 2.14 0.77 0.49 1.59
21.41 2.16 0.93 0.46 1.52
19.62 1.31 0.6 0.46 1.63
22.15 2.42 0.92 0.66 1.5
21.21 2.49 0.87 0.55 1.54
18.77 2.23 0.82 0.44 1.48
18.91 1.96 0.82 0.61 1.58
17.94 0.85 0.74 0.69 1.51
21.46 2.75 0.81 0.61 1.36
18.4 2.26 0.39 0.45 1.6
23.37 2.43 0.68 0.39 1.78
23.05 2.25 0.78 0.39 1.4
20.99 1.78 0.91 0.5 1.47
25.36 2.74 1.06 0.48 1.61
23.13 1.85 1.07 0.7 1.53
20.38 1.32 0.91 0.4 1.52
19.05 2.65 0.7 0.69 1.54
20.59 2.29 0.76 0.51 1.56
21.17 2.68 0.75 0.45 1.58
19.93 2.09 0.74 0.43 1.44
15.62 1.69 0.35 0.56 1.34
17.36 1.63 0.9 0.56 1.34
20.71 2.09 0.94 0.59 1.25
21.28 1.37 0.96 0.57 1.43
19.18 1.67 0.71 0.53 1.62
22.32 2.55 1.09 0.42 1.43
18.81 2.44 0.45 0.57 1.25
24.31 2.22 0.95 0.52 1.7
24.21 2.47 1.18 0.59 1.38
21.85 1.72 1.05 0.58 1.53
24.7 1.76 0.94 0.58 1.58
18.96 2.71 0.87 0.52 1.51
17.79 1.93 0.56 0.58 1.56
18.85 1.58 0.8 0.48 1.39
22.5 2.8 0.98 0.33 1.46
21.29 2.16 0.93 0.36 1.58
17.84 1.78 0.83 0.44 1.4
21.64 1.98 0.77 0.45 1.44
19.09 2.3 0.68 0.54 1.58
19.61 1.94 0.5 0.37 1.59
21.99 1.7 0.89 0.34 1.55
19.53 3.03 0.64 0.47 1.32
23.83 2.87 0.95 0.54 1.58
24.94 1.91 1.13 0.53 1.52
23.36 1.98 0.98 0.48 1.57
17.96 2.29 0.49 0.67 1.63
21.95 1.53 0.78 0.5 1.57
19.73 1.5 0.81 0.56 1.56
23.78 2.04 1.05 0.48 1.46
18.17 1.6 0.86 0.62 1.44
18.96 1.85 0.83 0.66 1.64
19.31 1.8 0.95 0.57 1.29
20.01 2.21 0.84 0.39 1.37
19.69 2.2 0.76 0.49 1.33
24.7 2.08 0.98 0.44 1.45
23.23 2.23 1.28 0.59 1.38
20.75 2.06 0.79 0.44 1.59
20.1 1.43 0.98 0.45 1.56
22.15 2.4 1.12 0.65 1.48
17.88 1.63 0.74 0.72 1.52
23.99 2.48 0.9 0.44 1.5
Explanation / Answer
Assuming Beta2 implies Coefficient of X2, please find solution below:
-> First Put the data into Excel
-> Make Y as last Column since this is Dependent Variable
-> Select Data Analysis tab, Select Regression and give input and output range for Y and X1, X2, X3 and X4
-> Select Confidence interval to 95% and Calculate
-> You wll get below results in new sheet:
So, Linear Regression Equation becomes:
Y = 1.646 + 1.258 * X1 + 7.950 * X2 + (-2.445)* X3 + 7.418 * X4
Hence, we get above coefficients.
Now, Beta2 = 7.950
For Beta2, 95% confidence interval is given as (6.387, 9.513)
Also, p-value of t-tes for Beta 2 is 0, So X2 is very significant variable.
Regression statistics is attached below in case you need:
ANOVA df SS MS F Significance F Regression 4.000 313.660 78.415 31.330 0.000 Residual 95.000 237.776 2.503 Total 99.000 551.436 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 1.646 2.577 0.639 0.525 -3.470 6.763 X Variable 1 1.258 0.392 3.213 0.002 0.481 2.035 X Variable 2 7.950 0.787 10.097 0.000 6.387 9.513 X Variable 3 -2.445 1.540 -1.588 0.116 -5.502 0.611 X Variable 4 7.418 1.413 5.248 0.000 4.612 10.224Related Questions
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