The following bivariate data below is assumed to follow a linear regression mode
ID: 3393047 • Letter: T
Question
The following bivariate data below is assumed to follow a linear regression model: y=+x This means that the data can be modeled as y i =+x i + i where the predicted dependent variable value for the i-th subject is y ˆ i =+x i and the residual (or error) is i .
y
Run the linear regression using the technology of your choice. With the output, report the following accurate to 3 decimal places:
correlation: r=
intercept: =
slope: =
y
1 53.3 54.9 2 45.7 60.2 3 46.2 55.1 4 39.9 56.5 5 58.6 57.2 6 62.2 64.8 7 45.5 63.4 8 44.8 62.4 9 49.9 59.8 10 59.7 68.7 11 36.5 57.2 12 36.2 54.6 13 46.7 51.8 14 73.7 67.8 15 57.8 63Explanation / Answer
Run the linear regression using the technology of your choice. With the output, report the following accurate to 3 decimal places:
correlation: r = 0.645
intercept: = 43.951
slope: = 0.315
Regression Analysis
r²
0.416
n
15
r
0.645
k
1
Std. Error
4.019
Dep. Var.
y
ANOVA table
Source
SS
df
MS
F
p-value
Regression
149.8596
1
149.8596
9.28
.0094
Residual
210.0097
13
16.1546
Total
359.8693
14
Regression output
confidence interval
variables
coefficients
std. error
t (df=13)
p-value
95% lower
95% upper
Intercept
43.9509
5.3147
8.270
1.55E-06
32.4691
55.4327
x
0.3147
0.1033
3.046
.0094
0.0915
0.5379
Regression Analysis
r²
0.416
n
15
r
0.645
k
1
Std. Error
4.019
Dep. Var.
y
ANOVA table
Source
SS
df
MS
F
p-value
Regression
149.8596
1
149.8596
9.28
.0094
Residual
210.0097
13
16.1546
Total
359.8693
14
Regression output
confidence interval
variables
coefficients
std. error
t (df=13)
p-value
95% lower
95% upper
Intercept
43.9509
5.3147
8.270
1.55E-06
32.4691
55.4327
x
0.3147
0.1033
3.046
.0094
0.0915
0.5379
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