Answered: After deciding on the appropriateness…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

After deciding on the appropriateness of a linear model relating coffee sales and maximum temperature, the managers calculate the equation of the least-squares regression line to be

=y−2553.5211.33x

. This is the line shown in the scatter plot above.
Based on the sample data and the regression line, complete the following.

(a)For these data, temperature values that are less than the mean of the temperature values tend to be paired with coffee sales values that are ▼(Choose one) the mean of the coffee sales values.

(b)According to the regression equation, for an increase of one degree in temperature, there is a corresponding ▼(Choose one) of

11.33

dollars in coffee sales.

(c)What was the observed coffee sales value (in dollars) when the temperature was

39.6

degrees Fahrenheit?

(d)From the regression equation, what is the predicted coffee sales value (in dollars) when the temperature is

39.6

degrees Fahrenheit? (Round your answer to at least one decimal place.)

Manage
an outdoor coffee stand in Coast City are examining the relationship between (hot) coffee sales and daily temperature, hoping to be able to predict
a day's total coffee sales from the maximum temperature that day. The bivariate data values for the coffee sales (denoted by y, in dollars) and the maximum
temperature (denoted by x, in degrees Fahrenheit) for each of randomly selected days during the past year are given below. These data are plotted in the
scatter plot below.
Temperature, Coffee sales,
(in degrees
Fahrenheit)
(in dollars)
67.5
1719.7
74.9
1984.8
2400-
39.0
2244.0
2200-
72.4
1667.1
2000 -
58.3
1927.0
55.6
1631.0
1800 -
71.0
1924.9
1600 -
39.6
2033.3
1400-
45.3
1821.1
1200
47.6
1995.2
50.1
2191.9
40
50
90
82.5
1533.0
Temperature, x
76.4
1549.6
(in degrees Fahrenheit)
62.2
1842.6
46.8
2165.4
Coffee sales, y
(in dollars)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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