Question

Topic: Linear Regression and Correlation

In the table offered the data related to:

Income	Activities
1,250	35
1,400	38
1.375	31
1,825	45
1,175	20
1,740	39

I. With the biweekly income variables and number of activities carried out by 6 people; find and analyze:

a) Linear dispersion diagram?

d) Correlation coefficient?

c) Perform a null hypothesis test that the correlation coefficients
Linear in the universe are not significantly different from zero. Present the six steps learned, with a significance level of 0.05, for the t & F test?

d) Linear regression equation for Ye?

e) Margin of error?

f) Estimation of the level of activities with an income of $ 1,600?

Answer 1

income <- c(1250,1400,1375,1825, 1175,1740) activities <- c(35,38,31,45,20,39) > # part a) linear disperson diagram > plot(activities, income, pch=16, main="linear disperson diagram") > # part b) correlation coefficient > correlation <- cor (activities, income) > correlation [1] 0.8167915 > # part c) > # HO: correlation coefficient is not linear > # V/S Hl: correlation coefficient is linear > cor.test(activities, income) Pearson's product-moment correlation data: activities and income t = 2.8315, df = 4, p-value = 0.04727 alternative hypothesis: true correlation is not equal to 0 95 percent confidence interval: 0.01551415 0.97923864 sample estimates : cor 0.8167915 > # interpretation: here p-value = 0.04727 which is less than 0.05, hence we reject HO, therefore given correlation coefficient is linear > # part d) linear regression > regression <- lm(income-activities) > regression Call: Tm(formula = income - activities) Coefficients: (Intercept) 587.2 activities 25.2

income 1200 1300 1400 1500 1600 1700 1800 25 activities linear disperson diagram 40 45