Answered

Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Experience the convenience of getting reliable answers to your questions from a vast network of knowledgeable experts. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

Using the Regression Calculator

John sells frozen fruit bars at a stand in a park during the summer months. He records the average weekly temperature and the number of frozen fruit bars sold for 6 weeks.

\begin{tabular}{|c|c|}
\hline Temperature [tex]$\left({ }^{\circ} F \right)$[/tex] & Fruit Bars Sold \\
\hline 67 & 50 \\
\hline 71 & 54 \\
\hline 76 & 63 \\
\hline 76 & 65 \\
\hline 82 & 65 \\
\hline 87 & 100 \\
\hline
\end{tabular}

1. What type of correlation exists between the temperature and the number of fruit bars sold?

A. Positive
B. Negative
C. No correlation

2. What is the real-world meaning of the slope of the line of best fit for the given scenario?

There are approximately [tex]$\square$[/tex] more fruit bars sold for every [tex]$\square$[/tex] degree(s) the temperature rises.

Sagot :

GinnyAnswer
To approach the problem of determining the correlation between temperature and the number of fruit bars sold, as well as understanding the real-world meaning of the slope of the line of best fit, we need to consider the following steps:

1. Determine the Correlation:
The correlation coefficient measures the strength and direction of a linear relationship between two variables. The correlation coefficient ranges from -1 to 1:
- A correlation close to 1 implies a strong positive correlation.
- A correlation close to -1 implies a strong negative correlation.
- A correlation close to 0 implies no linear correlation.

2. Calculate the Line of Best Fit:
The line of best fit is determined through linear regression, which calculates the best-fitting line through the data points. The equation of this line is:
[tex]\[ y = mx + b \][/tex]
where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the y-intercept.

3. Interpret the Slope:
The slope ([tex]\(m\)[/tex]) indicates the rate of change in the dependent variable (fruit bars sold) for each unit change in the independent variable (temperature).

Given the provided data for temperatures and the number of fruit bars sold:
[tex]\[ \begin{array}{|c|c|} \hline \text{Temperature} \left({ }^{\circ} F \right) & \text{Fruit Bars Sold} \\ \hline 67 & 50 \\ \hline 71 & 54 \\ \hline 76 & 63 \\ \hline 76 & 65 \\ \hline 82 & 65 \\ \hline 87 & 100 \\ \hline \end{array} \][/tex]

The correlation coefficient is calculated to be:
[tex]\[ 0.8928304366620293 \][/tex]
This value is close to 1, suggesting a strong positive correlation between temperature and the number of fruit bars sold.

The line of best fit has a slope ([tex]\(m\)[/tex]) of:
[tex]\[ 2.1854684512428295 \][/tex]
and an intercept ([tex]\(b\)[/tex]) of:
[tex]\[ -101.0216698534098 \][/tex]

### Real-World Meaning of the Slope
The slope of the line, approximately [tex]\(2.185\)[/tex], represents the change in the number of fruit bars sold for every unit increase in temperature. Specifically, this means:

"There are approximately [tex]\(2.185\)[/tex] more fruit bars sold for every [tex]\(1\)[/tex] degree Fahrenheit the temperature rises."

To make this a complete sentence:
There are approximately 2.185 more fruit bars sold for every 1 degree the temperature rises.
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.