Correlation and Regression Analyses

#4 (10points) Ms. Arceo studies if age correlates with the average number of hours of sleep, so she selected a random sample of size 11 and surveyed the needed data. age(x) 8 15 22 27 34 20 25 41 15 36 37 hours of sleep (y) Test the significance of the correlation coefficient at 0.01 level of significance. Correlation coefficient r: (a) For the sample data, there is a [b] correlation between age and number of hours of sleep. Testing significance of r STEP 1: Ho: There is [c] between age and number of hours of sleep. Ha: There is [d] between age and number of hours of sleep. STEP 2: a = 0.01 two tailed test df = [e] Critical value/s: [f] STEP 3: What is the computed test value? [g] STEP 4: Decision: [h] STEP 5: Conclusion: There is [i] between age and number of hours of sleep. [a] -0.5257 [e] 0.5256 10 -0.5258 11 -0.5250 8 [b] [f] +-2.821 low negative +-1.833 moderately high negative +-3.250 high negative +-3.690 moderately low negative [g] 1.584 [c] a significant relationship -1.854 no significant relationship -1.786 -1.845 [d] no significant relationship a significant relationship [h] Accept Ha Reject Ho Accept Ho Reject Ha [i] a significant relationship no significant relationship ates5 1 point A researcher investigated whether a mother's level of optimism was predictive of her daughter's optimism as a young adult. Twenty (20) mothers and daughters who agreed to participate in the study were administered a scale measuring their current level of optimism (the scale ranged from 10 to 50), with higher scores indicating greater optimism. Participant Mother Daughter 40 45 30 35 25 20 29 35 20 22 560 Va UA W N 25 35 46 48 49 39 46 49 23 38 35 26 28 16 19 29 45 46 31 49 41 37 31 18 31 36 19 42 45 20 43 48 1. Is the predictor significant? 2. What is the effect size for the study? 3. Based on your answer on the previous item, would you characterize the effect size as small, medium, or large? lippines)CHOICES OF #5 1. -Yes. Since the p-value of 0.01 is less than 0.05, mother's level of optimism is a significant predictor of her daughter's optimism as a young adult. - No. Since the p-value of 0.01 is less than 0.05, mother's level of optimism is a significant predictor of her daughter's optimism as a young adult. - No. Since the p-value of 0.001 is less than 0.05, mother's level of optimism is a significant predictor of her daughter's optimism as a young adult. - Yes. Since the p-value of 0.001 is less than 0.05, mother's level of optimism is a significant predictor of her daughter's optimism as a young adult. 2. -The effect size of the study is given by Adjusted R square = 0.41 indicating that 41% of the variance in daughter's level of optimism can be accounted for by knowing her mother's optimism. - The effect size of the study is given by t Stat = 3.75 indicating that 375% of the variance in daughter's level of optimism can be accounted for by knowing her mother's optimism. - The effect size of the study is given by R (multiple R) = 0.66 indicating that 66% of the variance in daughter's level of optimism can be accounted for by knowing her mother's optimism. - The effect size of the study is given by R square = 0.44 indicating that 44% of the variance in daughter's level of optimism can be accounted for by knowing her mother's optimism. 3. - small -medium -large -cannot be determined1 0.5 points If variable Y increases as variable X increases, then there is between variables X and Y. no significant difference a direct relationship a significant difference O an inverse relationship 2 0.5 points Determine the type of direction of correlation that you would expect of the given case / situation. Vaccinations and illness. O negative correlation no correlation zero correlation O positive correlation 3 0.5 points What are the data requirements when using Regression Analysis? One dependent variable and one independent discrete variable O One dependent variable and one independent continuous variable O One dependent discrete variable and one independent variable One dependent continuous variable and one independent variable