Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Get immediate and reliable answers to your questions from a community of experienced professionals on our platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
To determine the slope of the line of best fit, where [tex]\( x \)[/tex] represents the average daily temperature and [tex]\( y \)[/tex] represents the ice cream sales, we can follow these steps:
1. Identify the Data Points:
- The given data points are:
[tex]\[ \begin{array}{|c|c|} \hline \text{Temperature} (^{\circ}F) & \text{Ice Cream Sales} (\$) \\ \hline 58.2 & 112 \\ \hline 64.2 & 135 \\ \hline 64.3 & 138 \\ \hline 66.8 & 146 \\ \hline 68.4 & 166 \\ \hline 71.6 & 180 \\ \hline 72.7 & 188 \\ \hline 76.2 & 199 \\ \hline 77.8 & 220 \\ \hline 82.8 & 280 \\ \hline \end{array} \][/tex]
2. Formulate the Linear Model:
- We are looking for a linear relationship of the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
3. Compute the Slope [tex]\( m \)[/tex] of the Line of Best Fit:
- The slope [tex]\( m \)[/tex] can be determined from the formula for the line of best fit using methods like least squares regression. The formula for the slope [tex]\( m \)[/tex] is:
[tex]\[ m = \frac{N \sum (xy) - \sum x \sum y}{N \sum (x^2) - (\sum x)^2} \][/tex]
- Where [tex]\( N \)[/tex] is the number of data points, [tex]\(\sum (xy)\)[/tex] is the sum of the products of the paired data points, [tex]\(\sum x\)[/tex] and [tex]\(\sum y\)[/tex] are the sums of the [tex]\( x \)[/tex] and [tex]\( y \)[/tex] values respectively, and [tex]\(\sum (x^2)\)[/tex] is the sum of squares of the [tex]\( x \)[/tex] values.
4. Round the Slope to One Decimal Place:
- After calculation, we round the slope to one decimal place.
Given these calculations, the slope [tex]\( m \)[/tex] of the line of best fit turns out to be:
[tex]\[ m = 6.5 \][/tex]
Thus, the slope of the line of best fit, rounded to one decimal place, is [tex]\( 6.5 \)[/tex]. Therefore, the correct answer is:
[tex]\[ \boxed{6.5} \][/tex]
1. Identify the Data Points:
- The given data points are:
[tex]\[ \begin{array}{|c|c|} \hline \text{Temperature} (^{\circ}F) & \text{Ice Cream Sales} (\$) \\ \hline 58.2 & 112 \\ \hline 64.2 & 135 \\ \hline 64.3 & 138 \\ \hline 66.8 & 146 \\ \hline 68.4 & 166 \\ \hline 71.6 & 180 \\ \hline 72.7 & 188 \\ \hline 76.2 & 199 \\ \hline 77.8 & 220 \\ \hline 82.8 & 280 \\ \hline \end{array} \][/tex]
2. Formulate the Linear Model:
- We are looking for a linear relationship of the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
3. Compute the Slope [tex]\( m \)[/tex] of the Line of Best Fit:
- The slope [tex]\( m \)[/tex] can be determined from the formula for the line of best fit using methods like least squares regression. The formula for the slope [tex]\( m \)[/tex] is:
[tex]\[ m = \frac{N \sum (xy) - \sum x \sum y}{N \sum (x^2) - (\sum x)^2} \][/tex]
- Where [tex]\( N \)[/tex] is the number of data points, [tex]\(\sum (xy)\)[/tex] is the sum of the products of the paired data points, [tex]\(\sum x\)[/tex] and [tex]\(\sum y\)[/tex] are the sums of the [tex]\( x \)[/tex] and [tex]\( y \)[/tex] values respectively, and [tex]\(\sum (x^2)\)[/tex] is the sum of squares of the [tex]\( x \)[/tex] values.
4. Round the Slope to One Decimal Place:
- After calculation, we round the slope to one decimal place.
Given these calculations, the slope [tex]\( m \)[/tex] of the line of best fit turns out to be:
[tex]\[ m = 6.5 \][/tex]
Thus, the slope of the line of best fit, rounded to one decimal place, is [tex]\( 6.5 \)[/tex]. Therefore, the correct answer is:
[tex]\[ \boxed{6.5} \][/tex]
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.
