Question

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 are the OLS estimates calculated?

What does Gauss Markov theorem say about OLS estimates?

Suppose, you want to investigate what will happen to the demand of t-shirts if you increase price of the t-shirts that you are selling. Write down the regression model which will be able to investigate this relationship. From the theories that you have learnt in Principles of Micro, can you guess what curve are you estimating. What do you expect the relationship to be?

For each of the accompanying scatterplots for several pairs of variables, indicate whether you expect a positive or negative correlation coefficient between the two variables, and the likely magnitude of it (you can use a small range).

**(a)**

**(b)**

6. a) Suppose you are estimating the following regression:

Y=B1+ B2X +e.

Using the below data, calculate estimates of B1 and B2 and the
variance of B2.

b) Using your estimates, predict the value of y and the residual when x=3.

Answer #1

Answer for a)

ŷ = 33.75 + 1.45 MALE in this equation "MALE" is used as dummy which takes value 1 when Male is considered otherwise 0

Hence Average income of female is y_hat=33.75+1.45(0)=33.75

Answer for b)

And in case of male it should be y_hat(Male)=33.75+1.45(1)=35.2

Answer for c)

OLS stands for Ordinary least squares in which the error term that is the portion that moves away fromm population parameter we try to find minimum of sum of square of these error terms

For an example If Y=a+bX+error...(Y is dependant variable and X is independant variable i.e. value known to us and error term ) we can estimate only Y_hat=a+bx therefore (Y-Y_)^2=(error)^2 sum of these terms over the sample of observations.

Answer for d)

Gauss Markov theorem states that OLS estimats are consistent, efficient and unbiased.

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...

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?

Data needs to be analyzed
For this assignment I have to analyze the regression
(relationship between 2 independent variables and 1 dependent
variable). Below is all of my data and values. I need help
answering the questions that are at the bottom. Questions regarding
the strength of the relationship
Sum of X1 = 184.6
Sum of X2 = 21307.03
Sum of Y = 2569.1
Mean X1 = 3.6196
Mean X2 = 417.7849
Mean Y = 50.3745
Sum of squares (SSX1)...

You estimate a simple linear regression model using a sample of
25 observations and obtain the following results (estimated
standard errors in parentheses below coefficient estimates): y =
97.25 + 19.74 *x
(3.86) (3.42)
You want to test the following hypothesis: H0: beta2 = 1, H1:
beta2 >12. If you choose to reject the null hypothesis based on
these results, what is the probability you have committed a Type I
error?
a.)between .01 and .02 b.)between .02 and .05 c.)less...

The following table is the output of simple linear regression
analysis. Note that in the lower right hand corner of the output we
give (in parentheses) the number of observations, n, used
to perform the regression analysis and the t statistic for
testing H0: β1 = 0 versus
Ha: β1 ≠ 0.
ANOVA
df
SS
MS
F
Significance F
Regression
1
61,091.6455
61,091.6455
.69
.4259
Residual
10
886,599.2711
88,659.9271
Total
11
947,690.9167
(n = 12;...

1. You are given the following data to fit a simple linear
regression x 1 2 3 4 5 y -2 4 2 -1 0 Using linear least squares,
determine the t-value for testing the hypothesis that no linear
relationship exist between y and x. (a) 0.01, (b) 0.03, (c) 0.09,
(d) 0.11, (e) 0.13

II. You are given the following linear regression model, where
??2 represents a qualitative variable with two outcomes {0,1} and
??1 is a quantitative variable:
?? = ?0 + ?1??1 + ?2??2 + ?i
1. The response function for Y using ??2 = 0 is: (5pts)
2. The response function for Y using ??2 = 1 is: (5pts)
3. Explain theoretically what does
a) ?1 indicates. (10pts)
b) ?0 indicates (10pts)
c) ?2 indicates (10pts)

1. In a multiple
regression model, the following coefficients were obtained:
b0 = -10 b1
= 4.5 b2 = -6.0
a. Write the
equation of the estimated multiple regression model. (3 pts)
b Suppose a
sample of 25 observations produces this result, SSE = 480. What is
the estimated standard error of the estimate? (5 pts)
2. Consider the
following estimated sample regression equation:
Y = 12 + 6X1 -- 3 X2
Determine which of the following
statements are true,...

As a manager, you have been provided the following regression
summery output for a regression model of a new product.
PLEASE PROVIDE STEP BY STEP INSTRUCTIONS TO SOLVE THIS. THANK
YOU
df
SS
MS
F
Significance F
Regression
3
156.4823
52.16077
28.01892
0.000002177
Residual
26
48.4023
1.861627
Total
29
204.8846
Coefficients
P-value
Intercept
23.8163
9.24E-07
Price
-0.3035
0.001925
Price other
-0.342937
0.112442
Income
0.23406
0.033889
a. What is the percent risk of the coefficients really being
zero? In other words,...

Question 1
How is a residual calculated in a regression model? i.e. what is
the meaning of a residual?
a)The difference between the actual value, y, and the fitted
value, y-hat
b)The difference between the fitted value, y-hat, and the mean,
y-bar
c)The difference between the actual value, y, and the mean,
y-ba
d)The square of the difference between the fitted value, y-hat,
and the mean, y-bar
Question 2
Larger values of r-squared imply that the observations are more
closely...

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