Three entrepreneurial women open a shop selling high-quality second-hand childre
ID: 3068591 • Letter: T
Question
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.
(a) (3 marks) Identify the independent variable and the dependent variable in this example?
What type of variables are they?
(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?
(d) (3 marks) What is the value of the coefficient of determination and what does it mean in this example?
(e) (6 marks) Use the model described above to predict gross cash sales if 70 items are sold in a day. Is this prediction likely to be accurate? Explain briefly.
Gross cash sales for April 2004 $400.00 $350.00 $300.0o 2S250.00 i? $200.00 2 $150.00 $100.00 $50.00 y = 5.779x-0.719 R2 = 0.905 S- 10 20 30 40 50 60 Number of items soldExplanation / Answer
a) Independent Variable: Number of items sold in a day
Dependent Variable: Gross sales by cash payment in a day
b) Slope = 5.779
In this example slope means with 1 unit increase in the number of item sold the gross sale by cash will increase by $5.779
c) Intercept = -0.719
In this example intercept means when number of item sold is 0, the gross sale by cash will be $ -0.719.
d) R2 = 0.905
The coefficient of determination (R2) is a measure of the proportion of variance of a predicted outcome.
90.5% variation in Gross sales by cash payment is explained by the linear relationship between number of items sold in a day and Gross sales by cash payment.
e) No, this prediction is not likely to be accurate because 70 number of item sold is not in the given range of number of items. So we can not predict this value accurately.
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