Question

Ice Cream Sales vs Temperature Temperature °C | Ice Cream Sales 14.2° | $215 16.4° | $325 11.9° | $185 15.2° | $332 18.5° | $406 A. (10 points) Compute the correlation coefficient for the data, using the fact that the mean Temp is 15.2 degrees and the standard deviation is 2.5 degrees. The average sales are $293 and the standard deviation is $90.9. B. (10 points) Compute the slope and the intercept of the least squares regression line using temperature as X and sales as Y. C. (4 points) What is the expected change in sales for each additional degree in temperature? D. (6 points) Compute the predicted sales for a day that is 17 degrees. Can you predict the sales for a day that is 25 degrees? Explain. 5. (25 points total) Elephants sometimes damage crops in Africa. It turns out that elephants dislike bees. They recognize beehives in areas where they are common and avoid them. Can this be used to keep

          Ice Cream Sales vs Temperature
Temperature °C | Ice Cream Sales
14.2° | $215
16.4° | $325
11.9° | $185
15.2° | $332
18.5° | $406

A. (10 points) Compute the correlation coefficient for the data, using the fact that the mean Temp is 15.2 degrees and the standard deviation is 2.5 degrees. The average sales are $293 and the standard deviation is $90.9.

B. (10 points) Compute the slope and the intercept of the least squares regression line using temperature as X and sales as Y.

C. (4 points) What is the expected change in sales for each additional degree in temperature?

D. (6 points) Compute the predicted sales for a day that is 17 degrees. Can you predict the sales for a day that is 25 degrees? Explain.

5. (25 points total) Elephants sometimes damage crops in Africa. It turns out that elephants dislike bees. They recognize beehives in areas where they are common and avoid them. Can this be used to keep

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Ice Cream Sales vs Temperature
Temperature °C | Ice Cream Sales
14.2° | 215
16.4° |325
11.9° | 185
15.2° |332
18.5° | 406

A. (10 points) Compute the correlation coefficient for the data, using the fact that the mean Temp is 15.2 degrees and the standard deviation is 2.5 degrees. The average sales are293 and the standard deviation is 90.9.

B. (10 points) Compute the slope and the intercept of the least squares regression line using temperature as X and sales as Y.

C. (4 points) What is the expected change in sales for each additional degree in temperature?

D. (6 points) Compute the predicted sales for a day that is 17 degrees. Can you predict the sales for a day that is 25 degrees? Explain.

5. (25 points total) Elephants sometimes damage crops in Africa. It turns out that elephants dislike bees. They recognize beehives in areas where they are common and avoid them. Can this be used to keep

Added by Kristen L.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Teresa Wray

09/05/2022

Step 1

2 degrees Standard deviation of temperature (\( \sigma_x \)) = 2.5 degrees Mean ice cream sales (\( \bar{y} \)) = $293 Standard deviation of ice cream sales (\( \sigma_y \)) = $90.9 Using the formula: \[ r = \frac{\text{Covariance of X and Y}}{\text{Standard Show more…

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Ice Cream Sales vs Temperature Temperature °C | Ice Cream Sales 14.2° | $215 16.4° | $325 11.9° | $185 15.2° | $332 18.5° | $406 A. (10 points) Compute the correlation coefficient for the data, using the fact that the mean Temp is 15.2 degrees and the standard deviation is 2.5 degrees. The average sales are $293 and the standard deviation is $90.9. B. (10 points) Compute the slope and the intercept of the least squares regression line using temperature as X and sales as Y. C. (4 points) What is the expected change in sales for each additional degree in temperature? D. (6 points) Compute the predicted sales for a day that is 17 degrees. Can you predict the sales for a day that is 25 degrees? Explain. 5. (25 points total) Elephants sometimes damage crops in Africa. It turns out that elephants dislike bees. They recognize beehives in areas where they are common and avoid them. Can this be used to keep

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00:02 Okay, so we have the temperature and we have the ice cream.

00:04 They gave us the mean and standard deviation for each the temperature and the ice cream cells.

00:13 And we are using temperature as x and sales as y.

00:23 Before we can find the slope and the y intercept, we want to find the correlation.

00:28 So correlation is a real pain to calculate by hand.

00:34 So i suggest use an excel for your calculator.

00:39 I'm using excel and i just type in equals and then start typing in correlation.

00:45 And then it wants an array and another array.

00:48 So it's the first list, comma, my y list.

00:55 And that gives me the correlation of the data.

01:00 Okay.

01:01 Now to find the slope, i can use this formula here.

01:05 B is equal to r times the standard deviation of y over the standard deviation of x.

01:12 So i'm going to do my correlation times standard deviation of y, which is the ice cream sales, divided by standard deviation of x, which is the temperature.

01:31 So that gives me a slope of 34 .37.

01:37 So that means for each additional degree, ice cream cells go up by about 34 .37.

01:58 And what were they measuring it in? oh, dollars.

02:03 So about $34 and 37.

02:15 So each degree gets us another $34, give or take.

02:19 Okay, and then to find the y intercept, i'm going to do the mean of y.

02:26 So i have to do equals and the mean of y minus the slope times mean of x.

02:40 And that gives us a y intercept of negative 2, 29, 475.

02:47 Okay, so that takes care of our correlation and our slope and our y intercept...

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