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Answer :
Sure! Let's find the line of best fit for the given data, where [tex]\( x \)[/tex] represents the average daily temperature in degrees Fahrenheit, and [tex]\( y \)[/tex] represents the total ice cream sales in dollars.
The data points are:
- Temperature (°F): 58.2, 64.2, 64.3, 66.8, 68.4, 71.6, 72.7, 76.2, 77.8, 82.8
- Ice Cream Sales ([tex]$): 112, 135, 138, 146, 166, 180, 188, 199, 220, 280
### Steps to Determine the Line of Best Fit:
1. Identify the Variables:
- Let \( x \) be the temperature.
- Let \( y \) be the ice cream sales.
2. Use Linear Regression:
- We aim to find the equation of the line form \( y = mx + b \), where:
- \( m \) is the slope.
- \( b \) is the y-intercept.
3. Calculate the Slope (\( m \)) and Y-intercept (\( b \)):
- Using statistical tools or technology, we analyze the data points to calculate these values, ensuring they fit the data closely.
4. Round the Values:
- Round the slope and y-intercept to the nearest tenth for approximation.
### Result:
After performing the calculation, the line of best fit is given by:
\[ \hat{y} = 6.5x - 279.1 \]
- Slope (\( m \)) = 6.5: This means that for every increase of 1 degree Fahrenheit in temperature, ice cream sales are expected to increase by $[/tex]6.50.
- Y-intercept ([tex]\( b \)[/tex]) = -279.1: This value represents the expected ice cream sales when the temperature is 0°F, though it might not be directly interpretable within the context of our data.
This line provides the best prediction of ice cream sales based on the temperature data provided.
The data points are:
- Temperature (°F): 58.2, 64.2, 64.3, 66.8, 68.4, 71.6, 72.7, 76.2, 77.8, 82.8
- Ice Cream Sales ([tex]$): 112, 135, 138, 146, 166, 180, 188, 199, 220, 280
### Steps to Determine the Line of Best Fit:
1. Identify the Variables:
- Let \( x \) be the temperature.
- Let \( y \) be the ice cream sales.
2. Use Linear Regression:
- We aim to find the equation of the line form \( y = mx + b \), where:
- \( m \) is the slope.
- \( b \) is the y-intercept.
3. Calculate the Slope (\( m \)) and Y-intercept (\( b \)):
- Using statistical tools or technology, we analyze the data points to calculate these values, ensuring they fit the data closely.
4. Round the Values:
- Round the slope and y-intercept to the nearest tenth for approximation.
### Result:
After performing the calculation, the line of best fit is given by:
\[ \hat{y} = 6.5x - 279.1 \]
- Slope (\( m \)) = 6.5: This means that for every increase of 1 degree Fahrenheit in temperature, ice cream sales are expected to increase by $[/tex]6.50.
- Y-intercept ([tex]\( b \)[/tex]) = -279.1: This value represents the expected ice cream sales when the temperature is 0°F, though it might not be directly interpretable within the context of our data.
This line provides the best prediction of ice cream sales based on the temperature data provided.
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