A sample consists of 500 houses sold in Karachi between January 2020 and December 2020. The multiple linear regression analysis is carried out to predict the house prices for investment in residential properties in Karachi, Pakistan. The output below is produced using SPSS. (300 words) Table: Coefficients Model Unstandardized Coefficients t VIF Constant 14.208 5.736 Age of house -0.299 -2.322 1.58 Square footage of the house 0.364 2.931 1.71 Income of families in the area 0.004 0.392 1.01 Transportation time to major markets -0.337 -2.619 1.90 R2 = 0.67; DW = 2.08 Dependent Variable: House price (Pakistani rupees in Million) You are required to write the multiple regression How would you interpret the above ‘Output’ of a regression analysis performed in SPSS? From the above results, what can you say about the nature of autocorrelation? Is there multicollinearity in regression? How do you know?
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Q1:
A sample consists of 500 houses sold in Karachi between January 2020 and December 2020. The multiple linear
|
Model |
Unstandardized Coefficients |
t |
VIF |
|
Constant |
14.208 |
5.736 |
|
|
Age of house |
-0.299 |
-2.322 |
1.58 |
|
Square footage of the house |
0.364 |
2.931 |
1.71 |
|
Income of families in the area |
0.004 |
0.392 |
1.01 |
|
Transportation time to major markets |
-0.337 |
-2.619 |
1.90 |
|
R2 = 0.67; DW = 2.08 |
|
|
|
Dependent Variable: House price (Pakistani rupees in Million)
- You are required to write the multiple regression
- How would you interpret the above ‘Output’ of a regression analysis performed in SPSS?
- From the above results, what can you say about the nature of autocorrelation?
- Is there multicollinearity in regression? How do you know?
Q2.
a) Consider a model for firm profitability in a particular industry (say, automobile), where the
cross-section observations are at the country level. There are T months of data for each country.
???? ??????????????? = ? + ?1????????? ?????????? + ?2?????_19 ?????????? + ??? + ???
The variables in ??? are other factors affecting firm profitability, and Covid_19 pandemic is a
dummy indicator equal to one if the lockdown was eased in-country ? at time period t. You need
to explain how you would estimate this model; be specific about the assumptions/models you are
making. (200 words)
b) Let’s suppose that you have a set of time-series variables, and you want to model the relationship
between them. Read the situations given below and answer the questions. (200 words)
a) Explain the statistical test if the linear combination (of time-series variables) is I(0).
b) Which statistical test can be applied if all the series are integrated of the same order I(1).
Justify your answer
Q3.
How would you interpret the given output? (100 words)
|
Variables |
Cronbach’s Alpha |
Discriminant validity |
|||
|
Brand Image |
Brand Loyalty |
Brand Awareness |
Brand Equity |
||
|
Brand Image |
0.891 |
0.879 |
|
|
|
|
Brand Loyalty |
0.809 |
0.405 |
0.949 |
|
|
|
Brand Awareness |
0.836 |
0.210 |
0.183 |
0.878 |
|
|
Brand Equity |
0.952 |
0.145 |
0.360 |
0.198 |
0.872 |
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