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In: Math
The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals...
The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female). Ŷ = 30 + .7x1 + 3x2 Also provided are SST = 1200 and SSE = 384. The test statistic for testing the significance of the model is
Solutions
Expert Solution
$$ \begin{aligned} &\text { SSR }=\text { SST - SSE } \\ &=1200-384 \\ &=816 \\ &R^{2}=\frac{S S R}{S S T}=\frac{816}{1200}=0.68 \end{aligned} $$
milcah answered 2 years agoRelated Solutions
The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals...
The following estimated regression equation was developed
relating yearly income (y in $1000s) of 30 individuals
with their age (x1) and their gender
(x2) (0 if male and 1 if female).
Ŷ = 30 + .7x1 + 3x2
Also provided are SST = 1200 and SSE = 384. If we want to test for
the significance of the model, the critical value of F at
α = .05 is
a. 3.33.
b. 3.35.
c. 3.34.
d. 2.96.
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 following regression equation was estimated: Y = -2.0 + 4.6X. Please explain the meaning of...
The following regression equation was estimated: Y = -2.0 +
4.6X. Please explain the meaning of -2 and 4.6. What would be the
value of Y if X = 20.
Just 20 min
A hospital administrator developed a regression line, y = 30 + 2x, to predict y =...
A hospital administrator developed a regression line, y
= 30 + 2x, to predict y = the number of full-time
employees (FTE) needed using x = the number of beds. The
slope of this regression line suggests this: __________.
for a unit increase in the number of beds, the number of FTEs is
predicted to increase by 32
for a unit increase in the number of beds, the number of FTEs is
predicted to decrease by 32
for a unit...
A regression model was developed relating the 5-year average return (Y in %) of mutual funds...
A regression model was developed relating the 5-year average
return (Y in %) of mutual funds with two independent variables: Net
Asset Value and Expense Ratio (in %) of the funds. Part of the
regression results are shown below.
df
SS
MS
Regression
2
1197.092
598.546
Residual
34
1784.290
52.479
Total
36
2981.382
Coefficients
Standard Error
Intercept
0.280
3.221
Net Asset Value
0.171
0.085
Expense Ratio (%)
11.135
3.659
1. What is the value of the F test
statistic for testing...
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.
Determine the regression equation (write the regression equation) of the following data, where Y is the...
Determine the regression equation (write the regression
equation) of the following data, where Y is the dependant variable
and X is the predictor:
X
Y
5
85
4
103
6
70
5
82
5
89
5
98
6
66
6
95
2
169
7
70
7
48
b) Interpret the regression coefficients.
c) Graph the regression line.
d) Use the regression equation to predict Y for
X=3.
e) Compute the coefficient of
determination.
f) Interpret the coefficient of
determination.
g)...
A computer manufacturer has developed a regression model relating his sales (Y in $10,000s) with three...
A computer manufacturer has developed a regression model
relating his sales (Y in $10,000s) with three independent
variables. The three independent variables are price per unit
(Price in $100s), advertising (ADV in $1,000s) and the number of
product lines (Lines). Part of the regression results is shown
below.
Coefficient
Standard Error
Intercept
1.0211
22.8752
Price
-0.1524
0.1411
ADV
0.8849
0.2886
Lines
-0.1463
1.5340
Analysis of Variance
Source of
Variation
Degrees
of Freedom
Sum of
Squares
Regression
2708.61
Error (Residuals)
Required:...
A computer manufacturer has developed a regression model relating his sales (Y in $10,000s) with three...
A computer manufacturer has developed a regression model
relating his sales (Y in $10,000s) with three independent
variables. The three independent variables are price per unit
(Price in $100s), advertising (ADV in $1,000s) and the number of
product lines (Lines). Part of the regression results is shown
below.
Coefficient
Standard Error
Intercept
1.0211
22.8752
Price
-0.1524
0.1411
ADV
0.8849
0.2886
Lines
-0.1463
1.5340
Analysis of Variance
Source of
Variation
Degrees
of Freedom
Sum of
Squares
Regression
2708.61
Error (Residuals)
Required:...
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
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