The scatter plot demonstrates this regularity. Every regress or variable is normal. The relationship between the regress or variable and the response variable, y, is therefore linear.
A personnel officer in a governmental agency administered four newly developed aptitude test to each of 25 applicants for entry level clerical positions in the agency.
For purpose of the study, all 25 applicants were accepted for positions irrespective of their test scores.
The graph of the question is given below:
a) Stem and leaf plot
Stem-and-Leaf Display: x1
Stem-and-leaf of x1 N = 25
1 6 2
3 7 4 8
6 8 4 6 7
10 9 1 4 6 8
(7) 10 0 1 4 4 5 6 9
8 11 0 2
6 12 0 0 0
3 13 3
2 14 0
1 15 0
Stem-and-Leaf Display: x2
Stem-and-leaf of x2 N = 25
1 7 3
2 7 7
4 8 1 3
6 8 5 9
7 9 4
8 9 7
10 10 1 2
11 10 7
(3) 11 0 3 4
11 11 7 8 9
8 12 0 1 1 1 2
3 12 5 9 9
Stem-and-leaf of x3 N = 25
1 8 0
1 8
5 9 0 1 3 3
12 9 5 5 5 6 7 8 9
(4) 10 0 0 2 3
9 10 5 6 7 8 9
4 11 3 4
2 11 5 6
Stem-and-leaf of x4 N = 25
1 7 4
2 7 8
5 8 0 3 4
10 8 5 7 8 8 9
11 9 0
(3) 9 5 5 7
11 10 0 2 2 3 3 4
5 10 5 8 8 9
1 11 0
b) Scatter plot matrix is given below:
The scatter plot demonstrates this regularity. Every regress or variable is normal. The relationship between the regress or variable and the response variable, y, is therefore linear.
Correlation matrix
Correlation: x1, x2, x3, x4
x1 x2 x3
x2 0.102
x3 0.181 0.519
x4 0.327 0.397 0.782
c) Multiple regression equation
Regression Analysis: y versus x1, x2, x3, x4
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant -124.38 9.94 -12.51 0.000
x1 0.2957 0.0440 6.73 0.000 1.14
x2 0.0483 0.0566 0.85 0.404 1.37
x3 1.306 0.164 7.96 0.000 3.02
x4 0.520 0.132 3.94 0.001 2.83
Regression Equation
y = -124.38 + 0.2957 x1 + 0.0483 x2 + 1.306 x3 + 0.520 x4
The scatter plot demonstrates this regularity. Every regress or variable is normal. The relationship between the regress or variable and the response variable, y, is therefore linear.
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