Q3 (8 points) One would like to study the linear relationship between the score on a test (Y) with two potential factors X1 and X2 related to participants. The goal was to get a linear relationship as follows Y X1 X2 Regression Output from the Regression of Y on X1 and X2 1 68 78 2 75 74 3 85 82 377 73 ANOVA Table 76 Source Sum of Squares df Mean Square F-Test 79 Regression 590.69 27.08. Residuals 130.85 21.81 4 94 5 86 880 90 87 96 96 Coefficients Table 90 Variable Coefficient s.e. t-Test p-value 6 90 90 92 Constant -33.1627 18.7493 -1.769 0.127 7 86 83 95 X2 0.9820 0.3996 0.5110 1.922 0.103 0.3557 1.123 0.304 80 68 72 69 R2 = 0.9003 R2 = 0.867 8 = 4.67 9 55 68 88 67 Y = Bo+B1X1+ B2X2 +ε. (a) Calculate SSR and df in the ANOVA table. (1) (b) Suppose all required assumptions hold. Construct the 95% confidence interval for B2 and interpret the constructed confidence interval. (c) The potential-residual plot of fitting model (1) is shown as follows. Flag the outliers in the X-space and in the Y-space respectively (to avoid ambiguity, please flag the most extreme two, one for X-space and one for Y-space). 20- Potential-Residual Plot Residual (d) Calculate the Durbin-Watson statistics and test the null hypothesis Hop = 0 against an alternative H₁ p < 0 at significance level α = 0.05. (Use the closest value you can find in the distribution table)
Q3 (8 points) One would like to study the linear relationship between the score on a test (Y) with two potential factors X1 and X2 related to participants. The goal was to get a linear relationship as follows Y X1 X2 Regression Output from the Regression of Y on X1 and X2 1 68 78 2 75 74 3 85 82 377 73 ANOVA Table 76 Source Sum of Squares df Mean Square F-Test 79 Regression 590.69 27.08. Residuals 130.85 21.81 4 94 5 86 880 90 87 96 96 Coefficients Table 90 Variable Coefficient s.e. t-Test p-value 6 90 90 92 Constant -33.1627 18.7493 -1.769 0.127 7 86 83 95 X2 0.9820 0.3996 0.5110 1.922 0.103 0.3557 1.123 0.304 80 68 72 69 R2 = 0.9003 R2 = 0.867 8 = 4.67 9 55 68 88 67 Y = Bo+B1X1+ B2X2 +ε. (a) Calculate SSR and df in the ANOVA table. (1) (b) Suppose all required assumptions hold. Construct the 95% confidence interval for B2 and interpret the constructed confidence interval. (c) The potential-residual plot of fitting model (1) is shown as follows. Flag the outliers in the X-space and in the Y-space respectively (to avoid ambiguity, please flag the most extreme two, one for X-space and one for Y-space). 20- Potential-Residual Plot Residual (d) Calculate the Durbin-Watson statistics and test the null hypothesis Hop = 0 against an alternative H₁ p < 0 at significance level α = 0.05. (Use the closest value you can find in the distribution table)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Q3 (8 points) One would like to study the linear relationship between the score on a test (Y) with two
potential factors X1 and X2 related to participants. The goal was to get a linear relationship as follows
Y
X1
X2
Regression Output from the Regression of Y on X1 and X2
1
68
78
2
75
74
3
85
82
377
73
ANOVA Table
76
Source
Sum of Squares
df
Mean Square
F-Test
79
Regression
590.69
27.08.
Residuals
130.85
21.81
4
94
5
86
880
90
87
96
96
Coefficients Table
90
Variable
Coefficient
s.e.
t-Test
p-value
6
90
90
92
Constant
-33.1627
18.7493
-1.769
0.127
7
86
83
95
X2
0.9820
0.3996
0.5110
1.922
0.103
0.3557
1.123
0.304
80
68
72
69
R2 = 0.9003
R2 = 0.867
8 = 4.67
9
55
68
88
67
Y = Bo+B1X1+ B2X2 +ε.
(a) Calculate SSR and df in the ANOVA table.
(1)
(b) Suppose all required assumptions hold. Construct the 95% confidence interval for B2 and interpret the
constructed confidence interval.
Transcribed Image Text:(c) The potential-residual plot of fitting model (1) is shown as follows. Flag the outliers in the X-space
and in the Y-space respectively (to avoid ambiguity, please flag the most extreme two, one for X-space
and one for Y-space).
20-
Potential-Residual Plot
Residual
(d) Calculate the Durbin-Watson statistics and test the null hypothesis Hop = 0 against an alternative
H₁ p < 0 at significance level α = 0.05. (Use the closest value you can find in the distribution table)
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