Consumers are likely to purchase more of a good when the price of the good decreases, and vice versa.

As stated above, a marketing theory in the field of consumer behaviour believes that an indirect relation is likely to exist between the price and the number of units purchased for most of the goods and services. In examining this, you were commissioned as a student in the Business Data Analysis course to conduct a mock market research surveying a sample of potential customers in purchasing a hypothetical new product. You randomly selected 17 of your fellow students as the potential customers for the product. You questioned them on the number of units they were likely to purchase for a given price that you set. The data you collected from the mock survey are displayed below. You are tasked in performing the relevant inferential analyses on the relation between the two concerned variables by addressing the below set of questions.

Potential Customer	Set Price
		Number of units
		purchased
	in $
Kim	16.5	13
John	17	13
Phill	13.5	22
Patty	14.5	19
Sandy	21	16
Amy	22	13
Wayne	15	14
Adrienne	16.5	14
Damian	12	24
Nancy	13.5	22
Kirsten	17.2	14
Mary	17.5	15
Jane	19	17
Jimmy	19.5	16
jill	20	17
Smith	14.2	17
Sam	15	13

F) Provide interpretations of the slope coefficient and the intercept coefficient of the sample linear regression in terms of the relation between price and number of units purchased.

G) Predict the number of units purchased if price is $26. Display working. Comment on the validity of this prediction.

H) Calculate the coefficient of determination for the regression line. Provide an interpretation of the calculated coefficient of determination in terms of the relation between price and number of units purchased.

i) Perform the relevant hypothesis test at the 10% level of significance to see if a negative relation exists between price and number of units purchased. Display working of the six-steps of the hypothesis test. The t test-statistic has been calculated. t calculated = -2.59.