Question 1. A researcher wants to investigate the level of air pollution in a large city in relationto gasoline prices. Using the data from 1997 to 2018, the results are:Ý, = 32.4 - 496 X(15.42) (0.144)OLS SRF estimates:Standard errors:R? = 0.831,Standard error of regression (S) = 0.512,n= 22whereY, =the level of air pollution (in index points)X: = gasoline prices (in S per gallon)a. For this example, write the population regression function (PRF) and the sample regressionfunction (SRF). What are the population parameters in this example? What are the pointestimators in this example? Clearly explain.b. Referring back to part (a), what are the two components of Y, in the population regressionfunction, and what are the two components of Y in the sample regression function? Explainclearly how each component in the PRF relate to each component in the SRF.c. Clearly interpret 32.4 and-.496.d. Clearly interpret the coefficient of determination (R?).e. Test whether gasoline prices explain the behavior of air pollution. In answering, write the nulland alternative hypotheses and the decision rule. Show your calculations. State yourconclusion.f. State the assumption(s) that are needed for your answer to part (e) to be valid. g. Calculate the 90% confidence interval estimate of the population parameter of gasoline prices.Show your calculations. Interpret your result.h. Calculate the 90% confidence interval estimate of error variance (o). Show your calculations.Interpret your result.i. Use your result in part (h) to explain whether you reject the claim that the true standard errorof regression is 0.45 against the alternative that it is bigger than 0.45. In answering thisquestion, write the null and alternative hypotheses.j. State the assumption(s) that are needed for your answer to part (i) to be valid.k. List the steps in regression analysis. Have we taken all these steps in this example? Explainclearly.

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Question 1. A researcher wants to investigate the level of air pollution in a large city in relation to gasoline prices. Using the data from 1997 to 2018, the results are: OLS SRF estimates: Standard errors: Ý, = 32.4 - .496 X: (15.42) (0.144) R? = 0.831, Standard error of regression (S)3D0.512, n= 22

Question 1. A researcher wants to investigate the level of air pollution in a large city in relation to gasoline prices. Using the data from 1997 to 2018, the results are: OLS SRF estimates: Standard errors: Ý, = 32.4 - .496 X: (15.42) (0.144) R? = 0.831, Standard error of regression (S)3D0.512, n= 22

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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.

Question

g. Calculate the 90% confidence interval estimate of the population parameter of gasoline prices.
Show your calculations. Interpret your result.
h. Calculate the 90% confidence interval estimate of error variance (o). Show your calculations.
Interpret your result.
i. Use your result in part (h) to explain whether you reject the claim that the true standard error
of regression is 0.45 against the alternative that it is bigger than 0.45. In answering this
question, write the null and alternative hypotheses.
j. State the assumption(s) that are needed for your answer to part (i) to be valid.
k. List the steps in regression analysis. Have we taken all these steps in this example? Explain
clearly.

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