In: Advanced Math

An ice cream company collected data on their ice cream cones sales over a month in July in a Chicago suburb, along with daily temperature and the weather. The company is interested to develop a correlation between ice cream sales to the hot weather. Market research showed that more people come out in certain neighborhoods, to either enjoy the nice weather, or venture out if they do not have air conditioning in their apartments. The Chicago Police also tracked crime statistics during the same period. Crime statistics included murder, assault, robbery, battery, burglary, theft and motor vehicle theft. The data are shown below:

July |
Day Temp (F) |
Weather |
Ice cream sales (units) |
Crime stats reported |

1 |
83 |
Thunderstorm |
590 |
201 |

2 |
81 |
Thunderstorm |
610 |
220 |

3 |
84 |
Thunderstorm |
640 |
199 |

4 |
79 |
Partly sunny |
490 |
195 |

5 |
80 |
Mostly sunny |
550 |
187 |

6 |
84 |
Sunshine |
710 |
280 |

7 |
84 |
Sunshine |
690 |
261 |

8 |
86 |
Thunderstorm |
750 |
310 |

9 |
83 |
Shower |
720 |
254 |

10 |
86 |
Partly sunny |
850 |
300 |

11 |
83 |
Partly sunny |
690 |
219 |

12 |
84 |
Cloudy |
750 |
275 |

13 |
81 |
Thunderstorm |
450 |
156 |

14 |
82 |
Thunderstorm |
550 |
210 |

15 |
80 |
Heavy rain |
25 |
98 |

16 |
81 |
Heavy rain |
78 |
110 |

17 |
86 |
Sunshine |
790 |
256 |

18 |
81 |
Sunshine |
530 |
145 |

19 |
81 |
Sunshine |
490 |
199 |

20 |
80 |
Sunshine |
620 |
245 |

21 |
80 |
Sunshine |
690 |
260 |

22 |
79 |
Sunshine |
540 |
159 |

23 |
81 |
Partly sunny |
610 |
299 |

24 |
80 |
Partly sunny |
590 |
239 |

25 |
81 |
Partly sunny |
590 |
250 |

26 |
80 |
Sunshine |
580 |
200 |

27 |
87 |
Sunshine |
880 |
300 |

28 |
91 |
Sunshine |
1,059 |
361 |

29 |
90 |
Sunshine |
1,000 |
401 |

30 |
91 |
Partly sunny |
960 |
375 |

31 |
88 |
Partly sunny |
890 |
360 |

1.)Develop a linear regression model for ice cream sales over daily temperature. Show the linear equation in the form of y = ax + b, and the coefficient of determination.

What would be the projected forecast of ice cream sales in units, for daily temperature of 94 F?

2.) On July 15 & 16 there were heavy down pour of rain, which might have prevented some to venture out to purchase ice cream during the day. If you were to override those 2 data points, what would be the linear regression model be (by deleting July 15 & 16 data).

which would be considered a better forecast for ice cream sales

3.) Develop a linear regression on ice cream sales to crime statistics. Show the linear equation in the form of y = ax + b, and the r-square value.

Does this correlation demonstrate causation, that high ice cream sales cause crime statistics to go up?

An ice cream company collected data on their ice cream cones sales over a month in July in a Chicago suburb, along with daily temperature and the weather. The company is interested to develop a correlation between ice cream sales to the hot weather. Market research showed that more people come out in certain neighborhoods, to either enjoy the nice weather, or venture out if they do not have air conditioning in their apartments. The Chicago Police also tracked crime...

Jerry’s Ice Cream Parlor is considering a marketing plan to
increase sales of ice cream cones. The plan will give customers a
free ice cream cone if they buy 10 ice cream cones at regular
prices. Customers will be issued a card that will be punched each
time an ice cream cone is purchased. After 10 punches, the card can
be turned in for a free ice cream cone. Jerry Donovna, the
company’s owner, is not sure how the new...

Kilo-cone is an ice-cream store that sells 1kg ice cream cones,
and has the following information:
Estimated monthly Sales (in cones)
January to March: 45,000 per
month
April to September: 70,000 per month
October to December: 20,000 per month
Ice cream cones sell for $1 each from January 1st to
March 31st, and $3 each during the rest of the year.
Half of the sales are paid in cash, and the other half is on
account. 90% of the sales...

An ice cream shop sells five-scoop ice cream cones, allowing
customers to pick which flavors they want stacked on their cone.
The shop has the following ice cream flavors available: chocolate,
vanilla, strawberry, mint & chocolate chip, rocky road, cookies
& cream, cookie dough, cotton candy, butter pecan, birthday
cake, and cherry. Note that customers can order a five-scoop cone
with multiple scoops of the same flavor.
a) How many five-scoop cones are possible if order of the ice
cream...

Suppose that Dmitri and Frances are the only consumers of ice cream cones in a particular market. The following table shows their monthly demand schedules:
Price
Dmitri’s Quantity Demanded
Frances’s Quantity Demanded
(Dollars per cone)
(Cones)
(Cones)
1
8
14
2
5
10
3
3
6
4
1
3
5
0
1
On the following graph, plot Dmitri’s demand for ice cream cones using the green points (triangle symbol). Next, plot Frances’s demand for ice cream cones using the purple...

The daily demand for ice cream cones at a price of $1.20 per
cone is 50 cones. At a price of $2.20 per cone, the demand is 30
cones. Use linear interpolation to estimate the demand at a price
of $1.50 per cone.

Casper Ice Cream
The Casper Ice Cream Company is an ice cream manufacturer in
Richmond, Utah famous for making Fat Boy Ice Cream Sandwiches. The
owner, Mr. Casper, the grandson of the founder, is considering
replacing an existing ice cream maker and batch freezer with a new
maker which has a greater output capacity and operates with less
labor. His only alternative is to overhaul his ice cream maker and
batch freezer which have a current net book value of...

A random sample of 31 ice cream cones from McDonald's was
weighted, the sample mean weight was 3.5 ounces with a standard
deviation of 0.75 ounces. Construct a 99% confidence
interval to estimate the overall mean
weight of McDonald's ice cream cones. (Round your
intermediate steps to 4 decimal places, and final answer to 2
decimal places) (10 points)

After eating cookie dough ice cream and mixed berry ice cream
for a month,
Cookie Monster has decided that he wants just one ice cream that he
can
get that has both cookie dough and mixed berries. Linda and Tony
have
decided that they can combine the two ice creams together for their
best cus-
tomer. However, they want to make as much money as possible for
blending
these two together. They want to charge customers in proportion to
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The Chocolate Ice Cream Company and the Vanilla Ice Cream
Company have agreed to merge and form Fudge Swirl Consolidated.
Both companies are exactly alike except that they are located in
different towns. The end-of-period value of each firm is determined
by the weather, as shown below. There will be no synergy to the
merger.
State
Probability
Value
Rainy
.2
$
290,000
Warm
.3
470,000
Hot
.5
935,000
The weather conditions in each town are independent of those in...

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