Question

The manager of a seafood restaurant was asked to establish a pricing policy on lobster dinners. Experimenting with prices produced the following data:

Average Number Sold per Day, y	Price, x		Average Number Sold per Day, y	Price, x
200	$6.00		155	$8.25
190	6.50		156	8.50
188	6.75		148	8.75
180	7.00		140	9.00
170	7.25		133	9.25
162	7.50
160	8.00

Obtain a linear regression line for the above data, and use it to predict the number of lobster dinners expected to be sold. Specifically, what's your forecast for the number of lobster dinners expected to be sold with a given price of $7.75? (Round your answer to a whole number.)

Answer 1

a.Plot the data and a regression line on the same graph.

Answer :

X Price	Y Sales	X*Y	X2	Y2
6.00	200	1,200.00	36.00	40,000
6.50	190	1,235.00	42.25	36,100
6.75	188	1,269.00	45.56	35,344
7.00	180	1,260.00	49.00	32,400
7.25	170	1,232.50	52.56	28,900
7.50	162	1,215.00	56.25	26,244
8.00	160	1,280.00	64.00	25,600
8.25	155	1,278.75	68.06	24,025
8.50	156	1,326.00	72.25	24,336
8.75	148	1,295.00	76.56	21,904
9.00	140	1,260.00	81.00	19,600
9.25	133	1,230.25	85.56	17,689
92.75	1,982	15,081.50	729.05	332,142

Round b & a to two decimals:

Y = 316.12 – 19.53X

Actual data are represented by circles.

Predicted values are represented by pluses

Round r to four decimals:

b. Determine the correlation coefficient and interpret it.

Answer :

r = –0.9854 implies a strong, negative relationship between price and demand.

r2 = (–0.9854) 2 = 0.9700. It appears that 97.00% of the variation in sales can be accounted for by the price of our product. This indicates that price is a good predictor of sales.