Math Problem Statement
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Topic 7 Homework (Nonadaptive) Question 7 of 16 (1 point)|Question Attempt: 1 of Unlimited
Dennis
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Question 7 You are the owner of Fast Break, a popular local place that sells drinks, snacks, and sandwiches. For inventory management purposes, you are examining how the weather affects the amount of hot chocolate sold in a day. You are going to gather a random sample of 9 days showing that day's high temperature (denoted by x, in °C) and the amount of hot chocolate sold that day (denoted by y, in liters). You will also note the product ·xy of the temperature and amount of hot chocolate sold for each day. (These products are written in the row labeled "xy"). (a)Click on "Take Sample" to see the results for your random sample.
Take Sample High temperature, x (in °C) 12 18 23 7 29 12 23 3 15 Amount of hot chocolate sold, y (in liters) 10 7 11 16 5 15 8 18 12 xy 120 126 253 112 145 180 184 54 180
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Based on the data from your sample, enter the indicated values in the column on the left below. Round decimal values to three decimal places. When you are done, select "Compute". (In the table below, n is the sample size and the symbol Σxy means the sum of the values xy.)
n: x: y: sx: sy: Σxy:
Compute Sample correlation coefficient (r): Slope (b1): y-intercept (b0):
(b)Write the equation of the least-squares regression line for your data. Then on the scatter plot for your data, graph this regression equation by plotting two points and then drawing the line through them. Round each coordinate to three decimal places. Regression equation: y=
Amount of hot chocolate sold (in liters) y24681012141618202224x3691215182124273033360
High temperature (in °C)
(c)Use your regression equation to predict the amount of hot chocolate sold on a day with a high temperature of 19 °C. Round your answer to the nearest whole number. Predicted amount of hot chocolate sold: liters
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Math Problem Analysis
Mathematical Concepts
Statistics
Linear Regression
Correlation
Formulas
Sample correlation coefficient: r = (nΣxy - ΣxΣy) / √[(nΣx² - (Σx)²)(nΣy² - (Σy)²)]
Slope of regression line: b₁ = (nΣxy - ΣxΣy) / (nΣx² - (Σx)²)
Y-intercept: b₀ = (Σy/n) - b₁(Σx/n)
Theorems
Least Squares Regression Line
Suitable Grade Level
Grades 10-12
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