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Jordan plotted the graph below to show the relationship between the temperature of his city and the number of cups of hot chocolate he sold daily:
A scatter plot is shown with the title Jordans Hot Chocolate Sales. The x axis is labeled High Temperature and the y axis is labeled Cups of Hot Chocolate Sold. Data points are located at 20 and 20, 30 and 18, 40 and 20, 35 and 15, 50 and 20, 45 and 20, 60 and 14, 65 and 18, 80 and 10, 70 and 8, 40 and 2.
Part A: In your own words, describe the relationship between the temperature of the city and the number of cups of hot chocolate sold. (2 points)
Part B: Describe how you can make the line of best fit. Write the approximate slope and y-intercept of the line of best fit. Show your work, including the points that you use to calculate the slope and y-intercept. (3 points)
Bot GPT 3.5
answered
Part A: The relationship between the temperature of the city and the number of cups of hot chocolate sold seems to be somewhat scattered and not completely linear. There is a general trend that as the temperature increases, the number of cups of hot chocolate sold tends to decrease, but there are some fluctuations in the data points.
Part B: To make the line of best fit, we can first calculate the slope using the formula:
slope = (nΣ(xy) - ΣxΣy) / (nΣ(x^2) - (Σx)^2),
where n is the number of data points, Σ represents the sum of the values, and (x,y) are the data points. Using the data points provided, we get:
n = 11
Σx = 465
Σy = 145
Σxy = 7820
Σ(x^2) = 24195
Substitute these values into the formula, we get:
slope = (11*7820 - 465*145) / (11*24195 - 465^2) = 0.136
Next, we can calculate the y-intercept using the formula:
y-intercept = (Σy - slope*Σx) / n,
Substitute the values we have:
y-intercept = (145 - 0.136*465) / 11 = 2.909
Therefore, the approximate slope of the line of best fit is 0.136 and the y-intercept is 2.909.