Consider the following sample data Use Table 2 y 46 51 28 55 29 53 47 36 x 4048
ID: 3331020 • Letter: C
Question
Consider the following sample data Use Table 2 y 46 51 28 55 29 53 47 36 x 4048 29 44 30 58 60 29 x 13 28 24 11 28 28 29 14 a. Find the sample regression equation, y-hat bo + bxi+bx (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) 2281+ 085 xi + b. Construct a 95% confidence interval for EV if Xt equals 50 and x equals 20 (Round your intermediate celculations to 4 decimal places. tener vatue to 3 declmal places, and , answers to 2 decimal places.) Confidence intervall 45.39 to 56.61 c. Construct a 95% predict on intervalfory t equals 50 and X2 equals 20 (Round your intermediate calculations to 4 decimal places, ene value to 3 decimal places, and final answers to 2 decimal places.) Prediction interval to 64.29Explanation / Answer
Answer:
a).
y = 22.81+0.85*x1-0.71*x2
b).
95% CI = (45.39, 56.61).
c).
95% PI =(37.71, 64.29)
Regression Analysis
R²
0.863
Adjusted R²
0.808
n
8
R
0.929
k
2
Std. Error
4.687
Dep. Var.
y
ANOVA table
Source
SS
df
MS
F
p-value
Regression
693.0450
2
346.5225
15.78
.0069
Residual
109.8300
5
21.9660
Total
802.8750
7
Regression output
confidence interval
variables
coefficients
std. error
t (df=5)
p-value
95% lower
95% upper
Intercept
22.8074
6.8384
3.335
.0207
5.2288
40.3861
x1
0.8460
0.1523
5.555
.0026
0.4545
1.2376
x2
-0.7053
0.2451
-2.877
.0347
-1.3353
-0.0752
Predicted values for: y
95% Confidence Interval
95% Prediction Interval
x1
x2
Predicted
lower
upper
lower
upper
50
20
51.004
45.39
56.61
37.71
64.29
Regression Analysis
R²
0.863
Adjusted R²
0.808
n
8
R
0.929
k
2
Std. Error
4.687
Dep. Var.
y
ANOVA table
Source
SS
df
MS
F
p-value
Regression
693.0450
2
346.5225
15.78
.0069
Residual
109.8300
5
21.9660
Total
802.8750
7
Regression output
confidence interval
variables
coefficients
std. error
t (df=5)
p-value
95% lower
95% upper
Intercept
22.8074
6.8384
3.335
.0207
5.2288
40.3861
x1
0.8460
0.1523
5.555
.0026
0.4545
1.2376
x2
-0.7053
0.2451
-2.877
.0347
-1.3353
-0.0752
Predicted values for: y
95% Confidence Interval
95% Prediction Interval
x1
x2
Predicted
lower
upper
lower
upper
50
20
51.004
45.39
56.61
37.71
64.29