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.
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]

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