The following data set contains information on years of formal education and incomes in 2015. Row Education Income in in Years 2015 Dollars 1 7 22587 2 10 28305 3 12 40196 4 13 49483 5 14 54483 6 16 78073 7 18 99540 8 19 155646 9 21 125310 a. Estimate the regression equation Income = a + b(Education). b. What is the predicted increase in Income for a one-year increase in Education? c. What do you predict Income to be for a person who has 17 years of education? d. What fraction of the variation in Income is explained (or accounted for) by Education? e. Why do you think Income (in the data set) for 21 years of Education is lower than income with 19 years of education? f. Show the graph of the data with the equation for your regression line. g. Use the F statistic to test the hypothesis that there is no relation between Income and Education at the 5% level of significance. Do you reject this hypothesis or not? h. If you reject the hypothesis in the previous question, what is the probability that you are committing a Type I error (i.e., what is the probability of a false positive)?
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.
1. The following data set contains information on years of formal education and incomes in 2015.
Row Education Income in
in Years 2015 Dollars
1 7 22587
2 10 28305
3 12 40196
4 13 49483
5 14 54483
6 16 78073
7 18 99540
8 19 155646
9 21 125310
a. Estimate the regression equation Income = a + b(Education).
b. What is the predicted increase in Income for a one-year increase in Education?
c. What do you predict Income to be for a person who has 17 years of education?
d. What fraction of the variation in Income is explained (or accounted for) by Education?
e. Why do you think Income (in the data set) for 21 years of Education is lower than income with 19 years of education?
f. Show the graph of the data with the equation for your regression line.
g. Use the F statistic to test the hypothesis that there is no relation between Income and Education at the 5% level of significance. Do you reject this hypothesis or not?
h. If you reject the hypothesis in the previous question, what is the probability that you are committing a Type I error (i.e., what is the probability of a false positive)?
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