Statistics Worksheet # 6
Statistics Worksheet # 6.1Pearson Product Moment Correlation Coefficient If your calculated r = -1.17, what does that indicate?The correlation coefficient ralways lies between -1 and +1. So the calculation went wrong somewhere.Which shows a stronger relationship, a correlation coefficient of r = -.90 or r = + .30?r = -.90 shows a stronger relationship 3. In a a two tailed test, with alpha set at .05, and N = 25, what is the critical value for the Pearson r? (Hint, page 292)The critical value for t is ±2.0687The critical value for r is given by23 r1-r2=±2.068723r2=2.068721-r2r2=2.0687223+2.06872=0.1569r=±0.1569=0.3961The critical value of r is 0.3961If the correlation of ice cream sales and life guard activity is significant and positive, what can we conclude?An increase in life guard activity is associated with an increase in ice cream sales.What is the approximate value of the correlation coefficient for a dataset that is a large round scattering of XY data points in a scatter plot?The correlation coefficient is approximately 0.Why is non-linearity a potential problem for correlation?The correlation coefficient measures only the strength of linear relationship between two variables. So non linearity is a potential problem. If the correlation of hearing with age is r = -.65, what proportion of the variability in hearing is accounted for by age?r2=0.652=0.422542.25% of the variability in hearing is accounted for by age.What does R2 tell us? R2 is the proportion of variation in the dependent variable accounted for by the independent variable.Problem 1Complete the following two charts for the data below for questions 9-29SubjectXYZxZyZx Zy11213-0.30861-0.661620.2041822????0.3086070.296590.091533????1.6973371.6654692.8268624????0.1543030.296590.0457655????-0.61721-0.387850.2393866??-1.23443-1.209181.492639Total84107004.900364 Subject X X2 XY Y2 Y11214415616913?????????????????????????????????????????????????????????????????????Total841386173021751079. What is the null hypothesis?The null hypothesis is that the population correlation coefficient is 0H0:ρ=0What is the alternative or research hypothesis?The alternative hypothesis is that the population correlation coefficient is different from 0.H1:ρ≠011. N =612. df = 6-2=4 13. With an alpha level of .05 and a two-tailed test, what would be a significant correlation coefficient for the above scores (what is the critical value)? (hint: see page 292)The critical value of t on 4 df is ±2.7764The critical value for r is ±2.776424+2.77642=±0.6584=±0.811414. ?X =8415. ?X2 =138616. (?X)2 =705617. SSx =21018. sx= 6.480719. ?Y =10720. ?Y2 =217521. (?Y)2 = 1144922. SSy =266.833323. sy=7.3052For questions 24 and 25, use the formula found in your book that uses Z scores.24. ?ZxZy =4.900425. r =0.980126. Is correlation coefficient for the above data statistically significant?Yes. It is significant27. What do you conclude?X and Y are not independent. They are correlated.For questions 28 - 29, calculate ?XY and calculate Pearson r using one of the other methods from the lecture notes. Are your results the same?28. ?XY =173029. r =0.9801Problem 2Use the data below for questions # 30-50SubjectXYZxZyZx Zy157-1.23606-1.217011.504297215110.156683-0.72404-0.1134531212-0.26114-0.60080.1568934910-0.67896-0.847290.5752755620-1.096780.38513-0.4224618250.5745061.0013380.575275721200.9923290.385130.382176825301.5494251.6175462.506267?111135005.164332SubjectXX^2XYY^2Y152535497215225165121113121441441441249819010010563612040020618324450625257214414204002082562575090030Total11119012174273913530. What is the null hypothesis?The null hypothesis is that the population correlation coefficient is 0H0:ρ=031. What is the alternative or research hypothesis?The alternative hypothesis is the population correlation coefficient is not equal to 0.H1:ρ≠032. N =833. df = 634. With an alpha level of .05 and a two-tailed test, what would be a significant correlation coefficient for the above scores (what is the critical value)? (hint: see page 292)The critical value of t on 6 df is 2.4469The critical values for r are ±2.446926+2.44692=±0.706735. ?X =11136. ?X2 =190137. (?X)2 =1232138. SSx =360.87539. sx= 7.180140. ?Y =13541. ?Y2 =273942. (?Y)2 = 1822543. SSy =460.87544. sy=8.1141For questions 45 and 46, use the formula found in your book that uses Z scores.45. ZxZy =5.164346. r =0.737847. Is correlation coefficient for the above data statistically significant?It is statistically significant.48. What do you conclude?The two variables are correlated.For questions 49 - 50, calculate ?XY and calculate Pearson r using one of the other methods from the lecture notes. Are your results the same?49. ?XY =217450. r =0.7378Regression questions: 51. For the data presented in the Problem 2 Table, what proportion of the variance in Y is accounted for by the variance in X?r2=0.73782=0.5443The proportion of the variance in Y is accounted for by the variance in X =54.43%52. a is known as the _intercept____ and represents ______value of y when x = 0__.53. Y’ is known as the _estimate of y_____ and is used for ____prediction____.54. A health club conducted a survey and reported that the correlation between attendance to the club and fitness was r = +1.25. What is wrong with this correlation?Correlation coefficient cannot be greater than 155. In addition, a representative from the health club above said that these results show that exercise increases health. What is wrong with their conclusion?The computed correlation coefficient is wrong. So nothing can be said.56. In multiple regression, what is X always equal to where the regression line crosses the Y axis?X = 0 ................
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