Statistics Example Problem

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Please see the attached files.

Introduction
We are given data on two variables, annual wage in dollars and number of years of experience. The natural expectation is a positive relationship between the variables, i.e., as the years of experience increases the wage also increases. But, such intuitions need not be true always. Hence, one has to examine scientifically whether the expectation is true or not. Since the present problem is regarding the nature and degree of relationship between two variables, annual wage and years of experience, it can be addressed statistically, by using linear regression analysis.

Research Question
The research question to be addressed in this problem is, whether the given data support the claim that there exists a positive liner relationship between annual wage in dollars and the number of years of experience and hence the variations in the annual wages in dollars can be explained by the variations in the number of years of experience.

Methodology
In order to address the research question, we have to fit a simple linear regression model of the form Y = α + β X, where Y denotes the annual wage in dollars and X denotes the number of years of experience. We then examine the explanatory power and the statistical significance of the estimated model. The explanatory power of the model can be examined by using the coefficient of determination (R2) and the statistical significance by using either F test or t- test.

Hypothesis
The null hypothesis to be tested is that there is no statistically significant linear relationship between annual wages in dollars and the number of years of experience against the alternative hypothesis that there exists statistically significant linear relationship between annual wage in dollars and the number of years of experience.

Since we are dealing with a simple linear regression analysis problem, this hypothesis can be tested either by testing the statistical ...