Question
In: Advanced Math
1. Using the following table of relation between X & Y (Y is the independent Variable):...
1. Using the following table of relation between X & Y (Y is the independent Variable):
xi -2 2 4 5 4 6 7 8 11
yi -4 1 3 1 3 8 10 20 30
a. Find the estimated regression equation. Show ALL your calculations and the appropriate formula. WRITE Formula in all the questions below and substitute for the numbers, demonstrate your work.
b. Calculate R2. Comment on the Goodness of the Fit. Is it a good fit? Why?
c. Test the hypothesis regarding the significance of the slope β1. (Use α = 0.05) Show ALL the calculations necessary to get your answer. Hint: You need to calculate t by using all the formulas needed for it using t in the Formula Sheet.
d. Calculate the values of F, using formula for F statistics. e. Draw the scatter diagram and also your estimated regression line in a diagram.
Solutions
Colby Messinger answered 2 years agoRelated Solutions
Suppose we have the following data on variable X (independent) and variable Y (dependent): X Y...
Suppose we have the following data on variable X (independent)
and variable Y (dependent):
X
Y
2
70
0
70
4
130
a.) By hand, determine the simple regression equation relating Y
and X.
b.) Calculate the R-Square measure and interpret the result.
c.) Calculate the adjusted R-Square.
d.) Test to see whether X and Y are significantly related using
a test on the population correlation. Test this at the 0.05
level.
e.) Test to see whether X and Y...
Suppose we have the following data on variable X (independent) and variable Y (dependent): X Y...
Suppose we have the following data on variable X (independent)
and variable Y (dependent):
X Y
2 70
0 70
4 130
Test to see whether X and Y are significantly related using a
t-test on the slope of X. Test this at the 0.05 level.
Test to see whether X and Y are significantly related using an
F-test on the slope of X. Test this at the 0.05 level.
Suppose we have the following data on variable X (independent) and variable Y (dependent): X Y...
Suppose we have the following data on variable X (independent)
and variable Y (dependent):
X
Y
2
70
0
70
4
130
a.) By hand, determine the simple regression equation relating Y
and X.
b.) Calculate the R-Square measure and interpret the result.
c.) Calculate the adjusted R-Square.
d.) Test to see whether X and Y are significantly related using
a test on the population correlation. Test this at the 0.05
level.
e.) Test to see whether X and Y...
Suppose we have the following data on variable X (independent) and variable Y (dependent): X Y...
Suppose we have the following data on variable X (independent)
and variable Y (dependent):
X Y
2 70
0 70
4 130
By hand, determine the simple regression equation relating Y
and X.
Calculate the R-Square measure and interpret the result.
Calculate the adjusted R-Square.
Test to see whether X and Y are significantly related using a
test on the population correlation. Test this at the 0.05
level.
Test to see whether X and Y are significantly related using a...
You are given the following information about y and x: y x Dependent Variable Independent Variable...
You are given the following information about y and
x:
y
x
Dependent Variable
Independent Variable
5
15
7
12
9
10
11
7
Calculate the value of SSR, using the
formula.
Suppose we have the following data on variable X (independent) and variable Y (dependent): X Y...
Suppose we have the following data on variable X (independent)
and variable Y (dependent):
X
Y
2
70
0
70
4
130
(SOLVE ALL BY HAND, NOT BY USING EXCEL)
By hand, determine the simple regression equation relating Y
and X.
Calculate the R-Square measure and interpret the result.
Calculate the adjusted R-Square.
Test to see whether X and Y are significantly related using a
test on the population correlation. Test this at the 0.05
level.
Test to see whether...
The following information regarding a dependent variable (y) and an independent variable (x) is provided. y&nb
The following information regarding a dependent variable
(y) and an independent variable (x) is
provided.
y x
2 9
4 7
5 6
5 4
7 5
8 1
Determine the least squares estimate of the
y-intercept, slope, and coefficient of determination
(?2).
X is an independent standard uniform random variable X ∼ Uniform(0, 1) Y is an independent...
X is an independent standard uniform random variable X ∼
Uniform(0, 1)
Y is an independent standard uniform random variable Y ∼
Uniform(0, 1)
U = min(X, Y )
V = max(X, Y )
Find the correlation coefficient of V and U , ρ(U, V) =
Correlation(U, V).
The following data for the dependent variable, y, and the independent variable, x, have been collected...
The following data for the dependent variable, y, and the
independent variable, x, have been collected using simple random
sampling:
X
Y
10
120
14
130
16
170
12
150
20
200
18
180
16
190
14
150
16
160
18
200
Construct a scatter plot for these data. Based on the scatter
plot, how would you describe the relationship between the two
variables?
Compute the correlation coefficient.
Simple Linear The following information regarding a dependent variable (Y) and an independent variable (X) is...
Simple Linear The following information regarding a dependent
variable (Y) and an independent variable (X) is provided.
Y 4,5,9,12,14
X 8,5,3,2,1
a. For the above observations, plot a scatter diagram and
indicate what kind of relationship (if any) exist between x and
y
. b. Find the estimate simple linear relationship between x and
y
c. Find MSE
d. Find the coefficient of determination
e. Find and interpret the correlation coefficient
f. Use the F statistic to test for any...
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