Question
In: Statistics and Probability
4. How should a researcher specify a multiple linear regression model? In answering this question, you...
4. How should a researcher specify a multiple linear regression model? In answering this question, you should be sure to draw on your overall knowledge of econometrics in order to consider not only how a researcher should specify an initial model, but also how a researcher should assess the performance of an initial model and thereby iterate towards a final model.
Solutions
Expert Solution
In predictive analysis, multiple linear regression is used to describing data and to explain the relationship between one dependent variable and two or more independent variables. It consists of three stages: 1) analyzing the correlation and directionality of the data, 2) estimating the model, i.e., fitting the line, and 3) evaluating the validity and usefulness of the model.
Firstly, it might be used to identify the strength of the effect that the independent variables have on a dependent variable.
Secondly, it can be used to forecast the effects or impacts of changes. That is to say, multiple linear regression analysis helps us to understand how much the dependent variable will change when we change the independent variables.
Thirdly, multiple linear regression analysis predicts trends and future values. The multiple linear regression analysis can be used to get point estimates.
orchestra answered 1 year agoRelated Solutions
1. A multiple linear regression model should not be used if: A The variables are all...
1. A multiple linear regression model should not be used
if:
A The variables are all statistically significant.
B The coefficient of determination R2 is large.
C Both of the above.
D Neither of the above.
2. Consider a multiple linear regression model where the output
variable is a company's revenue for
different months, and the purpose is to investigate how the revenue
depends upon the company's advertising budget. The input variables
can be time-lagged so that the first input...
When we estimate a linear multiple regression model (including a linear simple regression model), it appears...
When we estimate a linear multiple regression model (including a
linear simple regression model), it appears that the calculation of
the coefficient of determination, R2, for this model can be
accomplished by using the squared sample correlation coefficient
between the original values and the predicted values of the
dependent variable of this model.
Is this statement true? If yes, why? If not, why not? Please use
either matrix algebra or algebra to support your reasoning.
Discuss the underlying assumptions of a simple linear regression model; multiple regression model; and polynomial regression.
Discuss the underlying assumptions of a simple linear regression
model; multiple regression model; and polynomial regression.
Give an example of omitted variable bias in a multiple linear regression model. Explain how you...
Give an example of omitted variable bias in a multiple linear
regression model. Explain how you would figure out the probable
direction of the bias even without collecting data on this omitted
variable. [3 marks]
What is the drawback of using the step_wise model in multiple linear regression? How is feature...
What is the drawback of using the step_wise model in multiple
linear regression?
How is feature importance addressed in decision trees?
Is there a guarantee that an ensemble method always outperforms
a simple decision tree? Elaborate on your answer.
The following is the estimation results for a multiple linear regression model: SUMMARY OUTPUT Regression...
The following is the estimation results for a multiple linear
regression model:
SUMMARY OUTPUT
Regression Statistics
R-Square
0.558
Regression Standard Error
(S)
863.100
Observations
35
Coeff
StdError
t-Stat
Intercept
1283.000
352.000
3.65
X1
25.228
8.631
X2
0.861
0.372
Questions:
Interpret each coefficient.
The following is the estimation results for a multiple linear regression model: SUMMARY OUTPUT Regression...
The following is the estimation results for a multiple linear
regression model:
SUMMARY OUTPUT
Regression Statistics
R-Square
0.558
Regression Standard Error
(S)
863.100
Observations
35
Coeff
StdError
t-Stat
Intercept
1283.000
352.000
3.65
X1
25.228
8.631
X2
0.861
0.372
Question:
1.
A. Write the fitted regression equation.
B. Write the estimated intercepts and slopes, associated with
their corresponding standard errors.
C. Interpret each coefficient.
In a multiple linear regression model with 2 predictors (X1and X2), &n
In a multiple linear regression model with 2 predictors
(X1and
X2), TRUE or FALSE
In a multiple linear regression model with 2 predictors
(X1and X2), then
SSR(X1)+SSR(X2|X1) =
SSTO–SSE(X1,X2) TRUE or FALSE
In a multiple linear regression model with 2 predictors
(X1and X2), if X1and
X2are uncorrelated, SSR(X1) =
SSR(X1|X2). TRUE or FALSE
In a multiple linear regression model with 2 predictors
(X1and X2), SSR(X1) +
SSR(X2|X1) = SSR(X2) +
SSR(X1|X2). TRUE or FALSE
In simple linear regression, then
(X’X)-1is 2x2. TRUE or FALSE
In simple linear regression, the hat-matrix is
2x2. TRUE or FALSE
Question 4 A simple linear regression model was used in order to predict y, duration of...
Question 4
A simple linear regression model was used in order to predict
y, duration of relief from allergy, from x,
dosage of medication. A total of n=10 subjects were given
varying doses, and their recovery times noted. Here is the R
output.
summary(lmod4)
##
## Call:
## lm(formula = y ~ x)
##
## Residuals:
## Min 1Q
Median 3Q
Max
## -3.6180 -1.9901 -0.4798 2.2048 3.7385
##
## Coefficients:
##
Estimate Std. Error t value Pr(>|t|)
## (Intercept)...
for stat students, model ( linear regression, multiple regression,factorial experiments,liner model) for each statistical method ,...
for stat
students,
model ( linear
regression, multiple regression,factorial experiments,liner
model)
for each
statistical method , why is the underlying statistical model
important ? more than 4 reasons.
please explain in clear way , i will discuss that with my class .
Thx
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