Question

psy230 flipped assignment 4- linear regression. thank you

PSY 230 Flipped Classroom Assignment: Linear Regression GRADED ASSIGNMENT Prompt: After finding an association between openness to experience and interest in statistics, the statistics instructor examined another personality trait: extraversion. Again, he hypothesizes that there would be a positive association between the two variables, such that greater levels of extraversion will be associated with greater levels of interest in statistics. To test this hypothesis, he used the same participants from his course (n168) and computed a linear regression model to predict statistics interest in future classes. The following variables were collected and computed as such: Extraversion: Two items were collected and averaged together to yield an extraversion score. Higher scores indicate more extraversion. The mean score was 3.98 (SD 1.51). The minimum and maximum values for openness were 1.00 and 7.00, respectively Extraversion (2 items; Internal Reliability -0.73) The possible range of scores for each component is between 1 and 7. Using the 7 response Extraverted, enthusiastic. scale, higher scores Reserved Interest in Statistics: Four items were collected and averaged together to yield an interest in statistics score. Higher scores indicate more interest in statistics. The mean score was 4.96 (SD 1.18). The minimum and maximum values for ss were 1.50 and 7.00 Interest in Statistics (4 items: Internal Reliability0.91) The possible range of scores for each component is between 1 and 7. Using the 7- response scale, higher scores then correspond to more positive I am interested in being able to communicate statistical information to others I am interested in using statistics I am interested in understanding statistical information. I am interested in leaning statistics. The stats instructor has given us all the components necessary for our analyses (see table below). Using all the information provided by the super-suave stats instructor compute the linear regression and give a report on your findings. Answer the following EX ExtraverExtraver Inter Inter EY sion est est EXY 833 4368. 3363 56 sion 668 50 75 1. State the null and research hypotheses (please put in sentences). 2. What is your predictor (independent variable) and what is your outcome (dependent variable) in the model? 3. Select the appropriate test statistic (ie., what analysis are you performing). Why did you choose that analysis? 4. Using the formula provided, compute the Slope (b). Show your work. 5. Using the formula provided, compute the Intercept (a). Show your work. 6. Using the linear regression notation (Y b(x)), notate the model you have just created (i.e., present your intercept and slope in regression notation). 7. Based on the linear regression model you created in question 6, find out what the predicted Y-value would be for a student who has an extraversion score of 1? What about 7? 8. Below is the output for the simple linear regression model we have created. Based on the output, is the slope statistically significant (p

Answer 1

1. Null hypothesis, Ho: there is no positive association between the twovariables i.e Extraversion and Interest is Statistics Alter native hypothesis, H1: there is a positive association between the twovariables 2. Independent variable- Extraversion, Dependent variable Interest is Statistics rn est statistic-t where. r = sample correlation coefficient 1-/2 and n- sample size 168 4. b(3363.13 668 833.75/168)/(3028.50 (668)2/168)0.1288 5. a = (833.75-0.1288 * 668)/168 4.4507 6. y 4.4507+0.1288x 7. When X-1, predicted Y - value4.45070.1288 1 4.5795 When X = 7, predicted Y-value = 4·4507+ 0.1288 * 7 = 5.3523 8. Since p value = 0.0341 < 0.05 hence the slope is statistically significant ie. significantly dif ferent from ero Σ x2ー(Σ x )2/168 = 3028.50-(668)2/168 = 372.4048 Srr = уг _ ( Y)2/ 168 4368.56 _ (833.75)2/168-230.8275 s,,- Sr,-〉 ㄨㄚ一(〉 X)(〉 y)/168= 3363.13-668 * 833.75/168-47.98 12

Standar dized estimate estimate of extraversion S0.1636 S. Since b = rPay-correlation coefficient between X and y .S 9. t = 2.1366 p - value-Pt> 2.136616 0.0170< 0.05 Hence we reject Ho at 5% level of significance and conclude that X and Y are positively associated.