Here we’ll use least squares (linear) regression to develop the total cost equat
ID: 3044318 • Letter: H
Question
Here we’ll use least squares (linear) regression to develop the total cost equation for a catering operation. This equation will be used along with revenue information to find the caterer’s break-even point.
Katie’s Catering Co. provides catering services for private dinner parties. To date, Katie has catered 17 dinner parties. The number of guests and total cost of catering each party are shown in the table below.
1. Make a scatter diagram of the data (Total Cost vs. Party Size).
Party Size
(# guests)
Total Cost
($)
63
1463
2. Find the least squares regression equation that gives Total Cost as a
45
1389
linear function of the Party Size.
120
3434
• The least squares regression equation here is:
50
1760
38
1760
92
2653
70
2281
3. Accurately plot the least squares regression line on your scatterplot
55
1649
either by hand (carefully) or by using the Excel’s Add Trendline tool.
110
3619
75
2467
80
2876
4. Based on the least squares regression equation, what is Katie’s:
40
1426
• Fixed cost of catering a dinner party?
64
1649
• Variable cost of serving dinner to a guest?
95
3136
68
1697
100
3396
60
2259
5. Is the linear relationship between Total Cost and Party Size weak, moderate or, strong?
because ________________________________ (support your answer with a number).
6. Suppose that Katie charges clients $42.99 per dinner party guest. Assuming that your regression
equation above accurately reflects Katie’s total costs, calculate her:
• BEPx (break-even point in # of guests):
• BEP$ (break-even point in dollars):
7. Suppose Katie agrees to cater a dinner party for 90 guests. What can Katie expect for the:
• Total cost of catering this party?
• Total profit from catering this party?
Please just help me with 6 and 7. Thanks and show step by step
1. Make a scatter diagram of the data (Total Cost vs. Party Size).
Party Size
(# guests)
Total Cost
($)
63
1463
2. Find the least squares regression equation that gives Total Cost as a
45
1389
linear function of the Party Size.
120
3434
• The least squares regression equation here is:
50
1760
38
1760
92
2653
70
2281
3. Accurately plot the least squares regression line on your scatterplot
55
1649
either by hand (carefully) or by using the Excel’s Add Trendline tool.
110
3619
75
2467
80
2876
4. Based on the least squares regression equation, what is Katie’s:
40
1426
• Fixed cost of catering a dinner party?
64
1649
• Variable cost of serving dinner to a guest?
95
3136
68
1697
100
3396
60
2259
5. Is the linear relationship between Total Cost and Party Size weak, moderate or, strong?
because ________________________________ (support your answer with a number).
Explanation / Answer
6)
As per the linear regression equation, the total cost equation is
Total cost = 199.49 + 28.999 * size
When Katie charges 42.99 per guest, her total sales is
Total sales = 42.99* size
to breakeven, total cost = total sales
13.99 size = 199.49
size = 14.25
she has to bring in 15 guests to break even.
total breakeven dollars = 14.25*42.99 = 612.93
7)
for 90 guests,
total cost = 199.49 + 28.999 * size
=199.49 + 28.999 * 90
=2809.32
total profit = sales - cost
if she charges 42.99 as per 6) then
total profit = 42.99*90 - 2809.32=1059.78