To find the slope of the line of best fit for the given data, we will follow these steps:
1. Data Collection:
- The given data for temperature (in degrees) and ice cream sales (in dollars) is as follows:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Temperature (ºF)} & \text{Ice Cream Sales (\$)} \\
\hline
61.0 & 107 \\
60.3 & 116 \\
64.2 & 120 \\
66.4 & 122 \\
71.3 & 125 \\
73.9 & 130 \\
74.2 & 132 \\
75.2 & 135 \\
80.1 & 151 \\
\hline
\end{array}
\][/tex]
2. Linear Regression Analysis:
- We will perform a linear regression analysis to find the best fit line [tex]\( y = mx + b \)[/tex] where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
3. Compute Slope and Y-Intercept:
- The slope (m) of the line of best fit is calculated using the formula:
[tex]\[
m = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}
\][/tex]
- The y-intercept (b) can be found using:
[tex]\[
b = \bar{y} - m\bar{x}
\][/tex]
where [tex]\( \bar{x} \)[/tex] and [tex]\( \bar{y} \)[/tex] are the means of the temperature and ice cream sales data respectively, and [tex]\( n \)[/tex] is the number of data points.
4. Given Results:
- The slope of the line of best fit (m) is approximately [tex]\( 1.7122883366705635 \)[/tex].
- When rounded to one decimal place, this result is [tex]\( 1.7 \)[/tex].
So, the slope of the line of best fit, rounded to one decimal place, is 1.7.
