The table shows the temperature (in degrees) for eight consecutive days as well as the respective number of ice cream cones an ice cream shop sold on each of these days.
Temperature: 68, 77, 83, 85, 89, 94, 96, 99
number of cones: 403, 447, 457, 465, 489, 503, 543, 576
About how many ice cream cones woud you expect the shop to sell if the temperature one day is 106 degrees? Find a line of best fit for this data and use it to make your prediction.
A. 579
B. 585
C. 602
D. 617
Sooooo nobody gone hep me??
chill dang
For anyone wanting to know in the future, its B: 585 cones.
Three years later. Thank you Sksksksk
You're welcome! It's never too late to get an answer.
To make a prediction about how many ice cream cones the shop would sell if the temperature is 106 degrees, we can use linear regression to find a line of best fit for the given data.
Linear regression is a statistical technique that allows us to find the equation of a straight line that best represents the relationship between two variables, in this case, temperature and number of ice cream cones sold.
To find the line of best fit for the given data, follow these steps:
1. Calculate the mean (average) of the temperature and the number of cones sold. Let's call them x̄ and ȳ, respectively.
x̄ = (68 + 77 + 83 + 85 + 89 + 94 + 96 + 99) / 8 = 87.25
ȳ = (403 + 447 + 457 + 465 + 489 + 503 + 543 + 576) / 8 = 495.25
2. Calculate the standard deviation of the temperature and the number of cones sold. Let's call them s(x) and s(y), respectively.
s(x) = √[((68 - 87.25)² + (77 - 87.25)² + (83 - 87.25)² + (85 - 87.25)² + (89 - 87.25)² + (94 - 87.25)² + (96 - 87.25)² + (99 - 87.25)²) / 7] ≈ 11.14
s(y) = √[((403 - 495.25)² + (447 - 495.25)² + (457 - 495.25)² + (465 - 495.25)² + (489 - 495.25)² + (503 - 495.25)² + (543 - 495.25)² + (576 - 495.25)²) / 7] ≈ 56.55
3. Calculate the correlation coefficient (r) between temperature and the number of cones sold.
r = Cov(x, y) / (s(x) * s(y))
Cov(x, y) = [(68 - 87.25)(403 - 495.25) + (77 - 87.25)(447 - 495.25) + (83 - 87.25)(457 - 495.25) + (85 - 87.25)(465 - 495.25) + (89 - 87.25)(489 - 495.25) + (94 - 87.25)(503 - 495.25) + (96 - 87.25)(543 - 495.25) + (99 - 87.25)(576 - 495.25)] / 7 ≈ 1220.21
r = 1220.21 / (11.14 * 56.55) ≈ 0.994
4. Using the calculated values x̄, ȳ, s(x), s(y), and r, we can find the equation of the line of best fit:
y = b * x + a
b = r * (s(y) / s(x)) ≈ 0.994 * (56.55 / 11.14) ≈ 5.05
a = ȳ - b * x̄ ≈ 495.25 - 5.05 * 87.25 ≈ 33.02
Therefore, the equation of the line of best fit is:
y ≈ 5.05 * x + 33.02
5. Now, we can substitute the given temperature of 106 degrees into the equation and calculate the predicted number of cones sold:
y ≈ 5.05 * 106 + 33.02 ≈ 537.3
Based on the line of best fit, we would expect the ice cream shop to sell approximately 537 ice cream cones if the temperature is 106 degrees.
However, since the answer choices provided are integers, we need to round this value to the nearest whole number.
Considering the rounded value, the closest option to 537 is option C. Therefore, the prediction would be:
C. 602 ice cream cones.
Patience is a virtue!
Your type of question is not easy to answer in this type of format, but surely
if you are asked this question by your teacher you must have learned some
kind of method to solve it. There are many ways, some very rigorous, some
rather straightforward.
Here is a video, in a rather boring presentation, that shows what you should do.
Too bad your data values are rather large numbers, so plotting them will
require some estimation right off the start.
good luck
https://www.youtube.com/watch?v=ugmhjwAQDIE