Question
In: Statistics and Probability
In a multiple linear regression with 40 observations, the following sample regression equation is obtained: yˆy^...
In a multiple linear regression with 40 observations, the
following sample regression equation is obtained:
yˆy^ = 12.5 + 2.4x1 − 1.0x2
with se = 5.41. Also, when
x1 equals 16 and x2 equals
5, se(yˆ0)se(y^0) = 2.60.
[You may find it useful to reference the t
table.]
a. Construct the 95% confidence interval for
E(y) if x1 equals 16 and
x2 equals 5. (Round intermediate
calculations to at least 4 decimal places,
"tα/2,df" value to 3 decimal places, and final
answers to 2 decimal places.)
b. Construct the 95% prediction interval for
y if x1 equals 16 and
x2 equals 5. (Round intermediate
calculations to at least 4 decimal places,
"tα/2,df" value to 3 decimal places, and final
answers to 2 decimal places.)
c. Which interval is wider?
-
Confidence interval since it does not include the variability caused by the error term.
-
Prediction interval since it includes the variability caused by the error term.
-
Confidence interval since it includes the variability caused by the error term.
-
Prediction interval since it does not include the variability caused by the error term.
Solutions
orchestra answered 1 year agoRelated Solutions
When estimating a multiple linear regression model based on 30 observations, the following results were obtained....
When estimating a multiple linear regression model based on 30
observations, the following results were obtained. [You may
find it useful to reference the t table.]
Coefficients
Standard Error
t Stat
p-value
Intercept
153.08
122.34
1.251
0.222
x1
12.64
2.95
4.285
0.000
x2
2.01
2.46
0.817
0.421
a-1. Choose the hypotheses to determine whether
x1 and y are linearly
related.
H0: β0 ≤ 0;
HA: β0 > 0
H0: β1 ≤ 0;
HA: β1 > 0
H0: β0 = 0;...
In a regression analysis involving 30 observations, the following estimated regression equation was obtained. ŷ =...
In a regression analysis involving 30 observations, the
following estimated regression equation was obtained.
ŷ = 17.6 + 3.2x1 − 2.2x2 +
7.6x3 + 2.7x4
1. Interpret b1 in this estimated regression
equation. (choose an option)
a)b1 = −2.2 is an estimate of the change in
y corresponding to a 1 unit change in
x1 when x2,
x3, and x4 are held
constant.
b)b1 = 7.6 is an estimate of the change in
y corresponding to a 1 unit change...
In a regression model involving 64 observations, the following estimated regression equation was obtained: Y=29+18X1+43X2+877X3 For...
In a regression model involving 64 observations, the following
estimated regression equation was obtained:
Y=29+18X1+43X2+877X3
For this model SSR=700 and SSE=500
Required:
a. Calculate the coefficient of determination for the above
model.
b. Calculate the correlation coefficient.
c- Calculate the MSR.
d. Calculate the computed F statistics for testing the
significance of the above model.
Linear regression equation
Linear regression equation also find accuracy Obtain regression equation of Y on X and estimate Y when X=55 from the following
Exercise 15-6 Algo When estimating a multiple linear regression model based on 30 observations, the following...
Exercise 15-6 Algo
When estimating a multiple linear regression model based on 30
observations, the following results were obtained. [You may
find it useful to reference the t table.]
Coefficients
Standard Error
t Stat
p-value
Intercept
153.35
126.57
1.212
0.236
x1
11.10
2.62
4.237
0.000
x2
2.36
2.06
1.146
0.261
a-1. Choose the hypotheses to determine whether
x1 and y are linearly related.
H0: β1 = 0;
HA: β1 ≠ 0
H0: β0 = 0;
HA: β0 ≠ 0
H0:...
Estimate the multiple linear regression equation for the given data 1 2 &n
Estimate the multiple linear regression equation
for the given data
1
2
3
4
10
1
2
3
12
18
24 30
Estimate the multiple linear regression equation y with
overparenthesis on top equals b subscript 0 plus b subscript 1 x
subscript 1 plus b subscript 2 x subscript 2 for the given
data
x subscript 1
1 2 3 4
x subscript 2
10 1 2 3
y
12 18 24 30
he following ANOVA table was obtained when estimating a multiple linear regression model. ANOVA df SS...
he following ANOVA table was obtained when estimating a multiple
linear regression model.
ANOVA
df
SS
MS
F
Significance F
Regression
2
22,009.81
11,004.905
0.0225
Residual
17
39,118.31
2,301.077
Total
19
61,128.12
a-1. How many explanatory variables were
specified in the model?
a-2. How many observations were used?
b. Choose the hypotheses to determine whether
the explanatory variables are jointly significant.
H0: β1 =
β2 = 0; HA: At
least one βj > 0
H0: β1 =
β2 = 0;...
The following is the estimation results for a multiple linear regression model: SUMMARY OUTPUT Regression...
The following is the estimation results for a multiple linear
regression model:
SUMMARY OUTPUT
Regression Statistics
R-Square
0.558
Regression Standard Error
(S)
863.100
Observations
35
Coeff
StdError
t-Stat
Intercept
1283.000
352.000
3.65
X1
25.228
8.631
X2
0.861
0.372
Questions:
Interpret each coefficient.
The following is the estimation results for a multiple linear regression model: SUMMARY OUTPUT Regression...
The following is the estimation results for a multiple linear
regression model:
SUMMARY OUTPUT
Regression Statistics
R-Square
0.558
Regression Standard Error
(S)
863.100
Observations
35
Coeff
StdError
t-Stat
Intercept
1283.000
352.000
3.65
X1
25.228
8.631
X2
0.861
0.372
Question:
1.
A. Write the fitted regression equation.
B. Write the estimated intercepts and slopes, associated with
their corresponding standard errors.
C. Interpret each coefficient.
Assignment on Multiple Linear Regression &nb
Assignment on Multiple Linear Regression
The Excel file BankData shows the values of the following
variables for randomly selected 93 employees of a bank. This real
data set was used in a court lawsuit against discrimination.
Let
= monthly salary in dollars (SALARY),
= years of schooling at the time of hire (EDUCAT),
= number of months of previous work experience (EXPER),
= number of months that the individual was hired by the bank
(MONTHS),
= dummy variable...
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