Suppose the simple linear regression model describes the following data: X = {10
ID: 3173048 • Letter: S
Question
Suppose the simple linear regression model describes the following data:
X = {10, 8, 6, 11, 4, 12} Y = {26, 25, 24, 14, 13, 34}
What is the value for S ?
What is the value for S^2 ?
At a used dealership, let X be an independent variable representing the age in years of a motorcycle and Y be the dependent variable representing the selling price of used motorcycle. The data is now given to you:
X = {5, 10, 12, 14, 15} Y = {500, 400, 300, 200, 100}
What is the value for S ?
What is the value for S^2 ?
Find the coefficient of correlation...
Find the coefficient of determination...
Explanation / Answer
Result:
Suppose the simple linear regression model describes the following data:
X = {10, 8, 6, 11, 4, 12} Y = {26, 25, 24, 14, 13, 34}
What is the value for S ? =7.655
What is the value for S^2 ? = 58.6018
Regression Analysis
r²
0.257
n
6
r
0.507
k
1
Std. Error
7.655
Dep. Var.
y
ANOVA table
Source
SS
df
MS
F
p-value
Regression
80.9263
1
80.9263
1.38
.3051
Residual
234.4070
4
58.6018
Total
315.3333
5
Regression output
confidence interval
variables
coefficients
std. error
t (df=4)
p-value
95% lower
95% upper
Intercept
11.5719
9.9450
1.164
.3093
-16.0399
39.1837
x
1.3053
1.1107
1.175
.3051
-1.7786
4.3891
At a used dealership, let X be an independent variable representing the age in years of a motorcycle and Y be the dependent variable representing the selling price of used motorcycle. The data is now given to you:
X = {5, 10, 12, 14, 15} Y = {500, 400, 300, 200, 100}
What is the value for S ? =52.537
What is the value for S^2 ? = 2760.0849
Find the coefficient of correlation...= -0.958
Find the coefficient of determination... 0.917
Regression Analysis
r²
0.917
n
5
r
-0.958
k
1
Std. Error
52.537
Dep. Var.
y
ANOVA table
Source
SS
df
MS
F
p-value
Regression
91,719.7452
1
91,719.7452
33.23
.0104
Residual
8,280.2548
3
2,760.0849
Total
100,000.0000
4
Regression output
confidence interval
variables
coefficients
std. error
t (df=3)
p-value
95% lower
95% upper
Intercept
728.0255
77.8791
9.348
.0026
480.1794
975.8715
x
-38.2166
6.6295
-5.765
.0104
-59.3146
-17.1185
Regression Analysis
r²
0.257
n
6
r
0.507
k
1
Std. Error
7.655
Dep. Var.
y
ANOVA table
Source
SS
df
MS
F
p-value
Regression
80.9263
1
80.9263
1.38
.3051
Residual
234.4070
4
58.6018
Total
315.3333
5
Regression output
confidence interval
variables
coefficients
std. error
t (df=4)
p-value
95% lower
95% upper
Intercept
11.5719
9.9450
1.164
.3093
-16.0399
39.1837
x
1.3053
1.1107
1.175
.3051
-1.7786
4.3891
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