Question

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).

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

                           [ 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?

Answer 1

The output is shown below

The linear regression model is Y = -3462.45 + 49.39X and the correlation coefficient is 0.77. Thus the correct answer will be "-3462.4 + 49.4(x); r^2 = .78"

Projected forecast with when X = 94 will be -3462.4 + 49.4*94 = 1181.2. Thus the correct answer will be 1181.

After deleting July 15 and 16 the output is shown below.

The linear regression model is Y = -2808.06 + 41.92X and the coefficient of determination is 0.85. Thus the correct answer will be "-2808.1 + 41.9(x); r^2 = .86"

Comparing the correlation coefficients, the correct answer will be

Second correlation is a better forecast

The output is show below

The regression model is Y = 46.78 + 0.3X and coefficient of determination is 0.81. Thus the correct answer will be "46.8 + .30(x); r^2 = .82"

No. Correlation does not imply causality