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?

b) 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

HEHEH y = 0.026 x - 4.007 R2 = 0.667 Activities 15 #HHHHHHHHHHHHHHHHHHH 1000 1200 1400 1600 1800 2000 Income (6) EXCEL (Data Analysis) output:

SUMMARY OUTPUT Regression Statistics Multiple R 0.816791467 R Square 0.6671483 Adjusted R Square 0.583935375 Standard Error 5.513660788 Observations ANOVA df Regression Residual Total 1 4 5 SS MS F S ignificance F 243.7315122 243.7315122 8.017363884 0.047273319 121.6018211 30.40045528 365.3333333 Intercept Income Coefficients -4.006517702 0.026473372 Standard Error t Stat p-value 13.84246162 -0.289436793 0.786629541 0.009349609 2.831494991 0.047273319 Lower 95% Upper 95% -42.4393525 34.4263171 0.000514695 0.052432049 The value of correlation coefficient is r = 0.8168. Null hypothesis:

Ho:p=0 The correlation coefficient is zero. Alternative hypothesis: H.:200 The correlation coefficient is not zero. EXCEL (Mega Stat) output: Correlation Matrix Income| Activities Income Activities 1.000 .817 1.000 6 sample size 1.811 critical value .05 (two-tail) 1.917 critical value .01 (two-tail)

Sincercat (=0.817) >ret (= 0.811), then reject the null hypothesis. Therefore, the correlation coefficient is not zero. Null hypothesis: H: B=0 Linear in the universe is zero. Alternative hypothesis: H.:B=0 Linear in the universe is different from zero. t-test: Since trec (= 2.831) >terit (= 2.776), then reject the null hypothesis. Linear in the universe is significantly different from zero.

F-test: Since p-value (=0.0473) sa(=0.05), then reject the null hypothesis. Linear in the universe is significantly different from zero. (d) The linear regression equation is j = -4.0065 +0.0265x.