PSYC1004 HW3 (Total mark = 26 marks) Instructions: Answer all the questions and use hand computations to obtain the answers for all questions involving computations. Remember to show your hand computations where applicable (marks will be given for them) for ALL questions and round your final answers to three decimal places. Please keep at least three decimal places throughout your hand computations to avoid rounding errors. Please submit a soft copy of your work to your tutor’s submission folder in the Moodle no later than 15th May, 5 pm. If you have any questions about HW3, please post it in the forum on Moodle. Question 1 [13 marks]: Sarah has surveyed 15 customers from a clothing store and found the following information on their age and expenditure on clothing purchase: X (Age) Y(Expenditure) 1 15 $200 2 35 $400 3 45 $350 4 22 $240 5 23 $300 6 21 $200 7 22 $380 8 28 $420 9 30 $550 10 55 $610 11 19 $180 12 38 $330 13 40 $410 14 33 $190 15 26 $660 You may use the following descriptive statistics for answering the questions below. Mean of X = 30 Standard deviation of X = 10.9 Mean of Y = $361 Standard deviation of Y = $153.1 a) Hand-calculate the sum of the cross products for the 15 cases. [2 marks] b) Hand-calculate the correlation coefficient of X (age) and Y (expenditure). [2 marks] c) Based on the correlation coefficient obtained in (b) above, comment on the relationship between X (age) and Y (expenditure).[2 marks] d) Hand-calculate the intercept and regression coefficient when expenditure is regressed on age. [4 marks] e) Sarah would like to use the customers’ age to predict their expenditure on clothing. Construct the regression equation (in the form of Ŷ= a + bX) for her. [1 mark] f) Based on the regression equation you have obtained in (e), predict the amount of expenditure for a customer not within the sample with the age of 33. [2 marks] Question 2 [13 marks]: Dr. Anderson recorded the body weight (measured in kg) and anxiety scores of his patients. The anxiety scores ranged from 0 to 21, with higher score meaning higher anxiety level. Dr. Anderson wanted to know if body weight can predict anxiety scores. Weight Anxiety scores 1 44 5 2 50 8 3 51 10 4 60 9 5 44 8 6 41 6 7 48 11 8 58 11 9 59 12 10 67 10 a) Produce a scatter plot using Excel of the bivariate distribution of the two variables for this sample, with variable X and Y along the horizontal and vertical axes respectively (The scatter plot needs to be clearly labelled). [3 marks] b) State the null and alternative hypotheses. [2 marks] c) Conduct an appropriate test using Jamovi to see if body weight can be used to predict anxiety scores. Report the conclusion in APA format. [6 marks] d) What is the proportion of variance in the dependent variable (anxiety scores) that can be explained by the independent variable (weight)?[2 marks]
