Question
In: Statistics and Probability
The following estimated regression equation based on 10 observations was presented. ŷ = 25.1670 + 0.5705x1...
The following estimated regression equation based on 10 observations was presented.
ŷ = 25.1670 + 0.5705x1 + 0.4960x2
Here, SST = 6,732.125, SSR = 6,221.375, sb1 = 0.0818, and sb2 = 0.0561.
a) Compute MSR and MSE. (Round your answers to three decimal places.)
MSR=
MSE=
Find the value of the test statistic. (Round your answer to two decimal places.)
F =
Perform a t test for the significance of β1. Use α = 0.05.
Find the value of the test statistic. (Round your answer to two decimal places.)
t =
Perform a t test for the significance of β2. Use α = 0.05.
Find the value of the test statistic. (Round your answer to two decimal places.)
t =
Solutions
orchestra answered 1 year agoRelated Solutions
The following estimated regression equation based on 10 observations was presented. ŷ = 21.1370 + 0.5903x1...
The following estimated regression equation based on 10
observations was presented.
ŷ = 21.1370 + 0.5903x1 +
0.4920x2
Here, SST = 6,736.125, SSR = 6,228.375,
sb1 =
0.0819,
and
sb2 =
0.0563.
(a)
Compute MSR and MSE. (Round your answers to three decimal
places.)
MSR=MSE=
(b)
Compute F and perform the appropriate F test.
Use α = 0.05.
State the null and alternative hypotheses.
H0: β1 <
β2
Ha: β1 ≥
β2
H0: β1 >
β2
Ha: β1 ≤
β2...
The following estimated regression equation based on 10 observations was presented. ŷ = 27.1570 + 0.5107x1...
The following estimated regression equation based on 10
observations was presented.
ŷ = 27.1570 + 0.5107x1 +
0.4940x2
Here, SST = 6,722.125, SSR = 6,223.375,
sb1 =
0.0811,
and
sb2 =
0.0569.
(a)
Compute MSR and MSE. (Round your answers to three decimal
places.)
MSR=MSE=
(b)
Compute F and perform the appropriate F test.
Use α = 0.05.
State the null and alternative hypotheses.
H0: β1 >
β2
Ha: β1 ≤
β2
H0: β1 =
β2 = 0
Ha: One...
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...
The estimated regression equation for these data is ŷ = 70 − 3x.
Consider the data.
xi
3
12
6
20
14
yi
55
35
60
10
25
The estimated regression equation for these data is
ŷ = 70 − 3x.
(a)
Compute SSE, SST, and SSR using equations
SSE = Σ(yi −
ŷi)2,
SST = Σ(yi −
y)2,
and
SSR = Σ(ŷi −
y)2.
SSE=
SST=
SSR=
(b)
Compute the coefficient of determination
r2. (Round your answer to three
decimal places.)
r2 =
(c)
Compute the sample correlation coefficient. (Round your answer...
Consider the following estimated regression equation, based on 10 observations. y^=29.1270+.5906x1+.4980x2 The values of SST and...
Consider the following estimated regression equation, based on
10 observations.
y^=29.1270+.5906x1+.4980x2
The values of SST and SSR are SST= 6724.125 and SSR = 6216.375,
respectively.
a) Compute the value of MSR. your answers to 3 decimal
places.
b) For the estimated regression equation given, compute
R2(multiple coefficient of determination).Round your
answers to 3 decimal places.
c) Predict a value of y when x1=180 and x2=310 (Round your
answers to 3 decimal places).
d) For the estimated regression equation given, compute...
The estimated regression equation for a model involving two independent variables and 10 observations follows. Here...
The estimated regression equation for a model involving two
independent variables and 10 observations follows. Here SST =
6,724.125, SSE = 507.75, sb1= 0.0813, and sb2= 0.0567.
= 29.1270 + 0.5906x1 +
0.4980x2
a. Interpret the regression coefficients in this estimated
regression equation.
b. Compute MSE.
c. Use the F test to determine the overall significance
of the relationship among the variables. Use α = 0.05.
d. Perform a t test for the significance of
x1. Use a 0.05 level...
The estimated regression equation for a model involving two independent variables and 10 observations follows. Here...
The estimated regression equation for a model involving two
independent variables and 10 observations follows. Here SST =
6,724.125, SSE = 507.75, sb1= 0.0813, and sb2= 0.0567.
= 29.1270 + 0.5906x1 +
0.4980x2
a. Interpret the regression coefficients in this estimated
regression equation.
b. Compute MSE.
c. Use the F test to determine the overall significance
of the relationship among the variables. Use α = 0.05.
d. Perform a t test for the significance of
x1. Use a 0.05 level...
Consider the data set below. Excel File: data12-33.xls The estimated regression equation is ŷ = 30.33...
Consider the data set below.
Excel File: data12-33.xls
The estimated regression equation is ŷ = 30.33 -
1.88x.
Estimate the standard deviation of ŷ p when
x = 3 (to 3 decimals).
Develop a 95% confidence interval for the expected value of
y when x = 3 (to 2 decimals).
( , )
Estimate the standard deviation of an individual value of
y when x = 3 (to 2 decimals).
Develop a 95% prediction interval for y wh
The regression equation is Ŷ = 30 + 2.56X, the sample size is 14, and the...
The regression equation is Ŷ = 30 + 2.56X, the sample size is
14, and the standard error of the slope is 0.97. What is the
critical value to test the significance of the slope at the 0.05
significance level?
Multiple Choice z = ±1.96
t = ±2.179
t = ±2.145
t = +2.145
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.
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