Answered

At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

\begin{tabular}{|l|l|}
\hline Temperature (°F) & Ice Cream Sales \\
\hline 58.2 & \[tex]$112 \\
\hline 64.2 & \$[/tex]135 \\
\hline 64.3 & \[tex]$138 \\
\hline 66.8 & \$[/tex]146 \\
\hline 68.4 & \[tex]$166 \\
\hline 71.6 & \$[/tex]180 \\
\hline 72.7 & \[tex]$189 \\
\hline 76.2 & \$[/tex]199 \\
\hline 77.8 & \[tex]$220 \\
\hline 82.8 & \$[/tex]280 \\
\hline
\end{tabular}

Using technology, determine the line of fit, where [tex]$x$[/tex] represents the average daily temperature and [tex]$y$[/tex] represents the total ice cream sales. Round values to the nearest tenth.

Sagot :

GinnyAnswer
Sure, let's go through the steps to determine the line of best fit for the given data, where [tex]\( x \)[/tex] represents the average daily temperature and [tex]\( y \)[/tex] represents the total ice cream sales. We aim to find a linear equation of the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.

### Step-by-Step Solution

1. Gather the Data:
- Temperatures: 8.2, 64.2, 64.3, 66.8, 68.4, 71.6, 72.7, 76.2, 77.8, 82.8
- Sales: 112, 135, 138, 146, 166, 180, 182, 199, 220, 280

2. Calculate the Line of Best Fit:
- Calculate the slope ([tex]\( m \)[/tex]) and the y-intercept ([tex]\( b \)[/tex]) using linear regression techniques.
- Use the least squares method to minimize the difference between the observed values and the values predicted by the linear equation.

3. Resulting Line of Best Fit:
- Slope ([tex]\( m \)[/tex]): After performing the least squares regression, we get the slope as 1.3 (rounded to the nearest tenth).
- Y-intercept ([tex]\( b \)[/tex]): The y-intercept is calculated to be 74.5 (rounded to the nearest tenth).

4. Correlation Coefficient ([tex]\( r \)[/tex]):
- The correlation coefficient gives an idea of how well the line fits the data.
- Here, the correlation coefficient ([tex]\( r \)[/tex]) is approximately 0.391. This value indicates a moderate positive relationship between temperature and ice cream sales.

5. Statistical Values:
- P-value: The p-value of 0.26395 suggests that there is a moderate probability that the relationship observed is due to random chance.
- Standard Error: The standard error of the slope is around 1.083, indicating the variability in the estimate of the slope.

### Summary

The equation of the line of best fit, with values rounded to the nearest tenth, is:

[tex]\[ y = 1.3x + 74.5 \][/tex]

Where:
- [tex]\( x \)[/tex] is the average daily temperature.
- [tex]\( y \)[/tex] is the total ice cream sales.

This equation can be used to predict ice cream sales based on the average daily temperature. If you have a temperature value, you can plug it into this equation to estimate the expected sales.
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.