Answer :
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.
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.
