Question
In: Statistics and Probability
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 Ra2(adjusted multiple coefficient of determination).Round your answers to 3 decimal places.
e) Compute p-value of the F test to test the following hypotheses
f) Compute the value of MSE. Round your answers to 3 decimal places.
e) Compute F-value (test statistic) of the F test to test the following hypotheses:
H0: β1=β2=0
Ha: One or more of the parameters is not equal to zero
Round your answers to 2 decimal places.
H0: β1=β2=0
Ha: One or more of the parameters is not equal to zero
Round your answers to 4 decimal places.
Solutions
orchestra answered 2 years 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 = 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....
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...
Given are five observations for two variables, x and y. The estimated regression equation for these...
Given are five observations for two variables, x and y. The
estimated regression equation for these data is y = 1 + 2.4x
(A) Compute SSE, SST, and SSR
(B) Compute the coefficient of determination, R^2.
(C) Compute the sample correlation coefficient.
x
y
1
3
2
8
3
5
4
12
5
13
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.
) Consider the following regression results based on 30 observations. y = 238.33 – 0.95x1 +...
) Consider the following regression results based on 30
observations.
y = 238.33 – 0.95x1 + 7.13x2 + 4.76x3; SSE = 3,439
y = 209.56 – 1.03x1 + 5.24(x2 + x3); SSE = 3,559
a. Formulate the hypotheses to determine whether the influences
of x2 and x3 differ in explaining y.
b. Calculate the value of the test statistic.
c. At the 5% significance level, find the critical value(s).
d. What is your conclusion to the test?
The estimated regression equation for a model involving two independent variables and 60 observations is: y...
The estimated regression equation for a model involving two
independent variables and 60 observations is: y ̂ = 30.17 - 2.5X1 +
0.428X2 Other statistics produced for analysis include: SSR =
1160.6, SST = 2183.4, Sb1 = 0.13, Sb2 = 0.20. Interpret
b1 and b2 in this estimated regression equation Predict y when X1 =
50 and X2 = 60. Compute R-square and Adjusted R-Square. Comment on
the goodness of fit of the model. Perform a “t” test using the...
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 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...
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