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# J L Question 4 (Total of 18 marks Three entrepreneurial women open a shop selling high-quality second-hand children's clothing, toys, and lmiture....

Three entrepreneurial women open a shop selling high-quality second-hand children's clothing, toys, and furniture. Items are consigned to the shop by individuals who then receive a percentage of the selling price of their items. Daily data for April 2004 was recorded, including each day's gross sales, broken down by the method of payment (cash or credit card). 'Gross sales' in retailing are overall dollar sales, not adjusted for returns or discounts. The data record the number of items sold and the dollar amount of gross sales for each payment method on the day. The three owners are interested in the relationship between the amount and the number of items sold for cash purchases.

The scatterplot of the data, together with the equation of a fitted regression line, is shown below.

J L Question 4 (Total of 18 marks» Three entrepreneurial women open a shop selling high-quality second-hand children’s
clothing, toys, and ﬁlmiture. Items are consigned to the shop by individuals who then receive
a percentage of the selling price of their items. Daily data for April 2004 was recorded,
including each day’s gross sales, broken down by the method of payment (cash or credit
card). ‘Gross sales’ in retailing are overall dollar sales, not adjusted for returns or discounts.
The data record the number of items sold and the dollar amount of gross sales for each
payment method on the day. The three owners are interested in the relationship between the
amount and the number of items sold for cash purchases. a The scatterplot of the data, together with the equation of a ﬁtted regression line, is shown
below. a Gross cash sales for April 2004 y : 5.7799X — 0.7192 2 : 0.9051 Gross cash sales Number of items sold
\ /.J (a) (3 marks) Identify the independent variable and the dependent variable in this example?lu
What type of variables are they? .J
(b) (3 marks) What is the value of the slope and what does it mean in this example?« (c) (3 marks) What is the value of the intercept and what does it mean in this example?« ((1) (3 marks) What is the value of the coefﬁcient of determination and what does it mean in
this example? .J (e) (6 marks) Use the model described above to predict gross cash sales if 60 items are sold
in a day. Is this prediction likely to be accurate? Explain brieﬂy. .J

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