y=63.1624x+163.9988 A) preidct the mean test 2 score for entering freshman who s
ID: 2946689 • Letter: Y
Question
y=63.1624x+163.9988
A) preidct the mean test 2 score for entering freshman who score (29) on the test 1.
B) Construct a 95% and 90% confidence interval for the mean test 2 score for entering freshmen who score a (29) on the test 1is lower bound and upper bound?
C) Construct a 95% prediction interval for the test 2 score for a randomly selected freshman who scores (29) on test the test 1 lower and upper bound?
Full data set Test 1, x 18 27 18 20 25 25 Test 2, y 1390 1340 1910 1150 1360 1780 1590 Test 1, x 19 17 28 30 20 18 Test 2, y 1470 1190 1770 2290 1660 1480 1370 The least-squares regression equation is y 63.1624x + 163.9988.Explanation / Answer
Result:
A) preidct the mean test 2 score for entering freshman who score (29) on the test 1.
B) Construct a 95% and 90% confidence interval for the mean test 2 score for entering freshmen who score a (29) on the test 1is lower bound and upper bound?
95% CI = (1813.883, 2177.533)
90% CI = (1846.974, 2144.443)
C) Construct a 95% prediction interval for the test 2 score for a randomly selected freshman who scores (29) on test the test 1 lower and upper bound?
95% PI= (1607.399, 2384.018)
Regression Analysis
r²
0.758
n
14
r
0.871
k
1
Std. Error
157.475
Dep. Var.
y
ANOVA table
Source
SS
df
MS
F
p-value
Regression
933,540.1709
1
933,540.1709
37.65
.0001
Residual
297,581.2576
12
24,798.4381
Total
1,231,121.4286
13
Regression output
confidence interval
variables
coefficients
std. error
t (df=12)
p-value
95% lower
95% upper
Intercept
163.9988
230.3558
0.712
.4901
-337.9035
665.9010
x
63.1624
10.2945
6.136
.0001
40.7327
85.5921
Predicted values for: y
95% Confidence Interval
95% Prediction Interval
x
Predicted
lower
upper
lower
upper
Leverage
29
1,995.708
1,813.883
2,177.533
1,607.399
2,384.018
0.281
Predicted values for: y
90% Confidence Interval
90% Prediction Interval
x
Predicted
lower
upper
lower
upper
Leverage
29
1,995.708
1,846.974
2,144.443
1,678.068
2,313.349
0.281
Regression Analysis
r²
0.758
n
14
r
0.871
k
1
Std. Error
157.475
Dep. Var.
y
ANOVA table
Source
SS
df
MS
F
p-value
Regression
933,540.1709
1
933,540.1709
37.65
.0001
Residual
297,581.2576
12
24,798.4381
Total
1,231,121.4286
13
Regression output
confidence interval
variables
coefficients
std. error
t (df=12)
p-value
95% lower
95% upper
Intercept
163.9988
230.3558
0.712
.4901
-337.9035
665.9010
x
63.1624
10.2945
6.136
.0001
40.7327
85.5921
Predicted values for: y
95% Confidence Interval
95% Prediction Interval
x
Predicted
lower
upper
lower
upper
Leverage
29
1,995.708
1,813.883
2,177.533
1,607.399
2,384.018
0.281
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