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.

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

[ Select ]                       [“-3892.2 + 40.1(x); r^2 = .78”, “-3462.4 + 49.4(x); r^2 = .78”, “-2362.5 + 39.2(x); r^2 = 0”, “-3432.6 + 41.3(x); r^2 = .61”]         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 correlation of determination (r^2).

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[ Select ]                       [“1201”, “1101”, “1001”, “1181”]         What would be the projected forecast of ice cream sales in units, for daily temperature of 94 F?

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[ Select ]                       [“-2808.1 + 41.9(x); r^2 = .86”, “-1362.5 + 33.2(x); r^2 = .67”, “-3932.6 + 51.3(x); r^2 = .93”, “-2892.2 + 60.1(x); r^2 = .55”]         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).

[ Select ]                       [“second correlation is a better forecast”, “need more data”, “no different”, “first correlation is a better forecast”]         Compare the two correlation coefficients, which would be considered a better forecast for ice cream sales

[ Select ]                       [“92.2 + 10.1(x); r^2 = .61”, “50.1 + 11.8(x); r^2 = .96”, “32.6 + .39(x); r^2 = .71”, “46.8 + .30(x); r^2 = .82”]         Develop a linear regression on ice cream sales to crime statistics. Show the linear equation in the form of y = ax + b, and the correlation of determination (r^2).

[ Select ]                       [“no, correlation does not imply causality”, “yes, strong correlation does imply causality”]         Does this correlation demonstrate causation, that high ice cream sales cause crime statistics to go up?

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