Question

Dose the scatter plot show a trend? If so, what is the trend?

Dose the scatter plot show a trend? If so, what is the trend? Temperature Ice Cream Sales 62 100 75 550 72 400 86 720 99 810 92 800 81 710 93 790 88 710 65 150 Group of answer choices Yes, the trend is inversely proportional. Yes, the trend is directly proportional. No, the trend is directly proportional. No, the trend is directly proportional. None of these

If there is a trend in the data, how many sales would you expect if the temperature outside is 90 degrees?

Temperature	Ice Cream Sales
62	100
75	550
72	400
86	720
99	810
92	800
81	710
93	790
88	710
65	150

Group of answer choices

500

None of these

750

There is no trend.

250

Answer 1

For this problem we use statistical software Minitab.

Part One:

Steps for minitab to draw scatter plot:

1) open minitab -> entry the temperature data in column C1 -> entry the ice cream sales data in column C2

2) Click on " Graph " menu -> Then chose " Scatterplots " -> Then chose " Simple "

3) Now select " Ice cream sales " as a " Y variables " -> And select " Temperature " as a " X variables "

4) Click on " Ok " -> And you get the " Scatter Plot "

Copied From MInitab:-

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From this scatter plot we clearly see that " Temperature " & " Ice Cream Sales " is " Highly Positively Correlated " so we get a directly proportional trend.

Correct Answer :- Yes, the trend is directly proportional.

Part Two:

Since there is " Directly Proportional " trend is present, then X-variable " Temperature " is a good predictor of Y-variable " Ice Cream Sales ". Now we find the regression equation of " Y On X " i.e. " Ice Cream Sales On Temperature ".

Steps for minitab to established the regression equation:

1) Open minitab -> entry the temperature data in column C1 -> entry the ice cream sales data in column C2

2) Click on " STAT " menu -> Then chose " Regression " -> Then again chose " Regression " -> Then chose    " Fit Regression Model "

3) Now select " Ice cream sales " as " Resposes " -> And select " Temperature " as " Continuous predictors "

4) Click on " Ok " -> And you get the " Regression Equation "

Copied from MInitab"-

Regression Equation

Ice Cream Sales = -1086 + 20.42 Temperature

Now, if the " Temperature " outside is 90 degrees then the Number of " Ice Cream Sales " is given by,

Putting the value of " Temperature = 90 " in regression equation, and we get

Ice Cream Sales = -1086 + 20.42 90 = 751.8  

So, if the " Temperature " outside is 90 degrees then the Number of " Ice Cream Sales " is 751.8

Correct Answer :- None of these or 750(approximately)