Question

Consider an estimated multiple regression model as given below.

log(y)ˆ=3.45+0.12log(x1)−0.42x2+0.36x3

Which of the following statements is correct in relation to the above estimated model?

1. If *x*_{3} increases by 1 unit,
*y* declines by 0.36

2. If *x*_{2} falls by 2 per cent,
log(*y*) decreases by 42percent

3. When the values of *x*_{1},
*x*_{2} and
*x*_{3} are three, the predicted value of
*y* is 5.2

4. f *x*_{1} increases by 1 percent,
*y* rises by 0.12 percent

Answer #1

we have give

log(y)ˆ=3.45+0.12log(x1)−0.42x2+0.36x3

1. this is false that If *x*3 increases by 1 unit,
*y* declines by 0.36 because If *x*3 increases by 1
unit, *y* increase by 0.36

2. this is false that If *x*2 falls by 2 per cent,
log(*y*) decreases by 42 percent

3. this is false that When the values of *x*1,
*x*2 and *x*3 are three, the predicted value of
*y* is 5.2

4. this is true that if *x*1 increases by 1 percent,
*y* rises by 0.12 percent beacuse it is true interpretation
of variable x1

so optio 4 is right choice

The estimated regression equation for a model involving two
independent variables and 10 observations follows.
Y= 30.7752 + 0.6659x1+ 0.3724x2
a. Interpret b1 and b2 in this estimated
regression equation.
b1= -------
Select your answer:
-y changes by 0.6659 when x1 increases by 1 unit and x2
stays the same
-y changes by 0.6659 when x2 increases by 1 unit and x1
stays the same
- y changes by 0.3724 when x1 increases by 1 unit and x2
stays the...

6. The following estimated regression model was developed
relating yearly income (Y in $1,000s) of 30 individuals with their
age (X1) and their gender (X2) (0 if male and 1 if female).
ˆ Y =20+0.7X1 +2X2 SST = 1,000 and SSE = 256
b) Is there a significant relationship between the yearly income
and the set of predictors (i.e., age and gender)? Use α=0.05 and
make sure to show all your steps.

2. Consider the data set has four variables which are Y, X1, X2
and X3. Construct a multiple regression
model using Y as response variable and other X variables as
explanatory variables.
(a) Write mathematics formulas (including the assumptions) and give
R commands to obtain linear
regression models for Y Xi, i =1, 2 and 3.
(b) Write several lines of R commands to obtain correlations
between Xi and Xj , i 6= j and i, j =
1, 2,...

Consider the multiple regression model E(Y|X1
X2) = β0 + β1X1 +
β2X2 +
β3X1X2
Can we interpret β1 as the change in the conditional
mean response for a unit change in X1 holding all the
other predictors in the model fixed?
Group of answer choices
a. Yes, because that is the traditional way of interpreting a
regression coefficient.
b. Yes, because the response variable is quantitative and thus
the partial slopes are interpreted exactly in that manner.
c. No,...

Regression model
Using gretl this has been estimated with the output below.
Model 1: OLS, using observations 1-57
coefficient
std. error
t-ratio
p-value
const
-0.6167
0.2360
-2.6130
0.0118
X1
-1.9892
0.0409
-48.6760
0.0000
X2
0.3739
0.0408
9.1686
0.0000
X3
1.3447
0.0368
36.5730
0.0000
X4
-0.4012
0.0320
-12.5220
0.0000
X5
-0.0478
0.1276
-0.3746
0.7095
Mean dependent var
-6.2529
S.D. dependent var
4.2151
Sum squared resid
6.8318
S.E. of regression
0.366
R-squared
0.99313
Adjusted R-squared
0.99246
F(5, 51)
1475.3
P-value(F)
0
Log-likelihood...

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,...

The following estimated regression model 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 + 0.7x1 + 3x2
Also provided are SST = 1200 and SSE = 384.
The estimated income of a 30-year-old male is _____.
a. $51
b. $510
c. $5100
d. $51,000

1.A real estate analyst has developed a multiple regression
line, y = 60 + 0.068 x1 – 2.5
x2, to predict y = the market
price of a home (in $1,000s), using two independent variables,
x1 = the total number of square feet of living
space, and x2 = the age of the house in years.
With this regression model, the predicted price of a 10-year old
home with 2,500 square feet of living area is __________.
$205.00
$255,000.00
$200,000.00...

An analyst is running a regression model using the following
data:
Y
x1
x2
x3
x4
x5
x6
4
1
5
0
-95
17
12
10
5
8
1
-27
7
10
32
1
7
0
-82
0
9
2
2
7
0
17
5
10
9
3
9
1
-46
5
11
Excel performs the regression analysis, but the output looks all
messed up: For example the F statistic cannot be computed, standard
errors are all zero, etc etc....

7)
Consider the following regression model
Yi = β0 + β1X1i + β2X2i + β3X3i + β4X4i + β5X5i + ui
This model has been estimated by OLS. The Gretl output is
below.
Model 1: OLS, using observations 1-52
coefficient
std. error
t-ratio
p-value
const
-0.5186
0.8624
-0.6013
0.5506
X1
0.1497
0.4125
0.3630
0.7182
X2
-0.2710
0.1714
-1.5808
0.1208
X3
0.1809
0.6028
0.3001
0.7654
X4
0.4574
0.2729
1.6757
0.1006
X5
2.4438
0.1781
13.7200
0.0000
Mean dependent var
1.3617
S.D. dependent...

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