Question

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?

Answer #1

In the simple linear regression model estimate Y =
b0 + b1X
A. Y - estimated average predicted value, X –
predictor, Y-intercept (b1), slope
(b0)
B. Y - estimated average predicted value, X –
predictor, Y-intercept (b0), slope
(b1)
C. X - estimated average predicted value, Y –
predictor, Y-intercept (b1), slope
(b0)
D. X - estimated average predicted value, Y –
predictor, Y-intercept (b0), slope
(b1)
The slope (b1)
represents
A. the estimated average change in Y per...

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...

CW 2
List 5 assumptions of the simple linear regression model.
You have estimated the following equation using OLS:
ŷ = 33.75 + 1.45 MALE
where y is annual income in thousands
and MALE is an indicator variable such that it is 1 for
males and 0 for females.
a) According to this model, what is the average income for
females?
b) According to this model, what is the average income for
females?
c) What does OLS stand for? How...

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***

Let us instead fit a linear regression model to the data on
employee sales. in particular, we fit the model: sales = b0 +
b1*employee group + e, where employee group is a categorical
variable with values a, b, and c. we set group a to be the
reference category. from this model we get the following
output. from this output,
1. what can we conclude is the mean sales for group a (in
dollars/day)?
2.what can you conclude is the...

The data file Demographics was used in a simple linear
regression model where Unemployment Rate is the response variable
and Cost of Living is the explanatory variable. You may refer to
the previous two questions for the regression model if you wish.
The anova function in R was used to obtain the breakdown of the
sums of squares for the regression model. This is shown below: >
anova(myreg)Analysis of Variance Table Response: Unemployment Df
Sum Sq Mean Sq F value...

1. A linear regression has the following equation: y = -9x + 2.
How much would y change by, if x increases by 4? Answer with a
positive number if y increases, and a negative number if y
decreases.
2.A linear regression has the following equation: y = -0.52x +
10, with a coefficient of determination R2 = 0.64. What is the
correlation coefficient, rounded to two decimal places?
3. A linear regression has the following equation: y = -0.36x...

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...

Consider a linear regression model with a response Y, and the
predictors, Based on a random sample of 25 observations, the
estimated model and other statistics are obtained as shown
below:
SST = 296458 and R-Square = 0.8803. What is the value of the
test statistic for testing the overall utility of this model? Round
your answers to the nearest ten-thousandth (4 decimals).

Suppose that a simple linear regression model is appropriate for
describing the relationship between y = house price (in
dollars) and x = house size (in square feet) for houses in
a large city. The population regression line is y = 22,500
+ 46x and σ = 5,000.
(a)
What is the average change in price associated with one extra
sq. ft of space?
$
What is the average change in price associated with an
additional 100 sq. ft of...

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