Question

which is the equation of the line of best fit for the given data?
temperature
ice cream sales
91
$230
69
$100
75
$180
77
$120
66
$120
84
$170
71
$160
85
$200
a
$y = 163.41x + 1.49$
b
$y = - 4.19x + 163.41$
c
$y = - 163.41x + 4.19$
d
$y = 4.19x - 163.41$
1 point

Explanation:

Step1: Analyze the relationship between temperature (x) and ice - cream sales (y)

As temperature (x) increases, we expect ice - cream sales (y) to increase. In a linear equation \(y = mx + b\), the slope \(m\) should be positive if there is a positive correlation.

Step2: Check the slopes of the given equations

• For equation \(y=-163.41x + 4.19\), the slope \(m=-163.41\) (negative). This would imply that as \(x\) (temperature) increases, \(y\) (sales) decreases, which is not logical for ice - cream sales.
• For equation \(y = - 4.19x+163.41\), the slope \(m=-4.19\) (negative). Again, a negative correlation which is incorrect for the relationship between temperature and ice - cream sales.
• For equation \(y = 163.41x+1.49\), if we assume \(x = 60\) (a reasonable temperature value), \(y=163.41\times60 + 1.49=9804.6 + 1.49 = 9806.09\), which is an unreasonably high value for ice - cream sales.
• For equation \(y = 4.19x-163.41\), when \(x = 60\), \(y=4.19\times60-163.41=251.4-163.41 = 87.99\); when \(x = 70\), \(y=4.19\times70-163.41=293.3 - 163.41=129.89\); when \(x = 80\), \(y=4.19\times80-163.41=335.2-163.41 = 171.79\). This equation shows a positive correlation (positive slope \(m = 4.19\)) and more reasonable sales values.

Answer:

\(y = 4.19x-163.41\) (assuming the option labeled as \(D\) in the original multiple - choice setup)