Question

**In the simple linear regression model estimate Y =
b_{0} + b_{1}X**

A. *Y* - estimated average predicted value, *X* –
predictor, *Y-intercept* (*b _{1}*), slope
(

B. *Y* - estimated average predicted value, *X* –
predictor, *Y-intercept* (*b _{0}*), slope
(

C. *X* - estimated average predicted value, Y –
predictor, *Y-intercept* (*b _{1}*), slope
(

D. *X* - estimated average predicted value, Y –
predictor, *Y-intercept* (*b _{0}*), slope
(

**The slope ( b_{1})
represents**

A. the estimated average change in Y per unit change in X.

B. variation around the line of regression.

C. predicted value of Y when X = 0.

D. the predicted value of Y.

**If the Durbin-Watson statistic has a value close to 0,
which assumption is violated?**

A. Homoscedasticity.

B. Independence of errors.

C. Normality of the errors.

D. None of the above.

**The standard error of the estimate is a measure
of**

A. total variation of the Y variable.

B. the variation of the X variable.

C. explained variation.

D. the variation around the sample regression line

**The coefficient of determination
( r^{2}) tells us**

A. that the coefficient of correlation (*r*) is larger
than 1.

B. the proportion of total variation that is explained.

C. whether *r* has any significance.

D. that we should not partition the total variation.

Answer #1

**In the simple linear regression model estimate Y =
b_{0} + b_{1}X**

*B. Y* - estimated average predicted value, *X* –
predictor, *Y-intercept* (*b _{0}*), slope
(

**The slope ( b_{1})
represents**

A. the estimated average change in Y per unit change in X.

**If the Durbin-Watson statistic has a value close to 0,
which assumption is violated?**

A. Homoscedasticity.

**The standard error of the estimate is a measure
of**

D. the variation around the sample regression line

**The coefficient of determination
( r^{2}) tells us**

B. the proportion of total variation that is explained.

5. You have performed a simple linear regression model and ended
up with Y(Y with a hat) = b0 + b1 x.
(a) In your own words, describe clearly what the coefficient of
determination, r^2, measures.
(b) Suppose that your calculations produce r^2 = 0.215. As
discussed in textbook, what can you conclude from this value?
Furthermore, what can you say about the strength and direction of
the relationship between the predictor and the response
variable?

The linear regression equation, Y = a +
bX, was estimated. The following computer printout was
obtained:
Given the above information, the value of the
R2 statistic indicates that
0.3066% of the total variation in X is explained by the
regression equation.
30.66% of the total variation in X is explained by the
regression equation.
0.3066% of the total variation in Y is explained by the
regression equation.
30.66% of the total variation in Y is explained by the
regression...

Here is the "theoretical" regression equation: yi =
β0 + β1xi + εi 1.
Select the appropriate name for each component of the equation.
yi: ---Select--- The linear correlation
coefficient
The population intercept The estimated intercept
The population slope
The estimated slope The LOBF
The "random error" term
The predictor variable
The response variable
The confounding variable
The sampling bias
β0: ---Select--- The linear correlation
coefficient
The population intercept
The estimated intercept
The population slope
The estimated slope The LOBF
The "random...

13. Interpreting the intercept in a simple linear
regression model is: *
(A) reasonable if the sample contains values of x
around the origin.
(B) not reasonable because researchers are interested in the
effect of a change in x on the change in y.
(C) reasonable if the intercept’s p-value is less than
0.05.
(D) not reasonable because it is always meaningless.
14. Which of the following is NOT one of the assumptions
necessary for simple linear regressions?: *
(A)...

Suppose that your linear regression model includes a constant
term, so that in the linear regression model
Y = Xβ + ε
The matrix of explanatory variables X can be
partitioned as follows: X = [i X1]. The
OLS estimator of β can thus be partitioned
accordingly into b’ = [b0
b1’], where b0 is
the OLS estimator of the constant term and
b1 is the OLS estimator of the slope
coefficients.
a) Use partitioned regression to derive formulas for...

Linear Regression conception
the true regression model is Y=B0+B1X+esilon
However, the sample simple regression line is
Y_head=B0_head+B1_headX, and it doesn't have the error esilon, but
why .Please explain it step by step and with some proof to
support
***follow the comment***

1. Consider the model Ci= β0+β1 Yi+ ui. Suppose you run this
regression using OLS and get the following results: b0=-3.13437;
SE(b0)=0.959254; b1=1.46693; SE(b1)=21.0213; R-squared=0.130357;
and SER=8.769363. Note that b0 and b1 the OLS estimate of b0 and
b1, respectively. The total number of observations is
2950.According to these results the relationship between C and Y
is:
A. no relationship
B. impossible to tell
C. positive
D. negative
2. Consider the model Ci= β0+β1 Yi+ ui. Suppose you run this...

A study is conducted to determine the simple linear regression
relation (if any) between average temperature over a week and
ice-cream sales in a particular city. The following table provides
the regression data required to construct the model:
Average Temperature and Ice-cream Sales
Average Temperature
over a Week (°F)
Weekly Ice-cream Sales
($'000s)
38
95.512
78
139.092
39
96.298
49
108.688
89
152.288
56
116.48
71
132.61
70
130.454
95
159.834
72
133.896
96
159.75
55
114.594
Calculate the slope...

Consider a linear regression model where y represents
the response variable, x is a quantitative explanatory
variable, and d is a dummy variable. The model is
estimated as yˆy^ = 15.4 + 3.6x −
4.4d.
a. Interpret the dummy variable
coefficient.
Intercept shifts down by 4.4 units as d changes from 0
to 1.
Slope shifts down by 4.4 units as d changes from 0 to
1.
Intercept shifts up by 4.4 units as d changes from 0 to
1.
Slope shifts...

Consider the simple linear regression model y=10+30x+e where the
random error term is normally and independently distributed with
mean zero and standard deviation 1. Do NOT use
software. Generate a sample of eight observations, one each at the
levels x= 10, 12, 14, 16, 18, 20, 22, and 24.
Do NOT use software!
(a) Fit the linear regression model by least squares and find
the estimates of the slope and intercept.
(b) Find the estimate of ?^2 .
(c) Find...

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