The table below shows the average temperature in a particular city for the months of March through October. Let xequals3 represent​ March, xequals4 represent​ April, and so on. Plot the points and then find a regression equation that best models the data.
March
April
May
June
July
August
September
October
46
50
55
58
59
57
52
47
Question content area bottom
Part 1
Choose the correct plot below. All graphs are left bracket 0 comma 12 comma 1 right bracket by left bracket 40 comma 60 comma 2 right bracket.
A.



x y graph
Your answer is correct.B.



x y graph
C.



x y graph
Part 2
The regression equation is yequals
  
enter your response here.
​(Type an expression using x as the variable. Use integers or decimals for any numbers in the expression. Round to the nearest thousandth as​ needed.)

### Part 1: Plotting the Points

Given the data### Part 1: Plotting the Points

Given the 

- March \((x = 3)\): \(y = 46\)
- April \((x = 4)\): \(y = 50\)
- May \((x = 5)\): \(y = 55\)
- June \((x = 6)\): \(y = 58\)
- July \((x = 7)\): \(y = 59\)
- August \((x = 8)\): \(y = 57\)
- September \((x = 9)\): \(y = 52\)
- October \((x = 10)\): \(y = 47\)

The points to plot on the graph are: 

\[
(3, 46), (4, 50), (5, 55), (6, 58), (7, 59), (8, 57), (9, 52), (10, 47)
\]

Given the plots, the correct graph is **A**, where the points follow a generally increasing pattern up to a peak and then decrease.

### Part 2: Finding the Regression Equation

Let's calculate the regression equation using the data points provided. The equation of the regression line is typically of the form:

\[
y = mx + b
\]

Where \(m\) is the slope and \(b\) is the y-intercept. I'll compute the linear regression using the least squares method.

Let me calculate it for you.### Regression Equation
The regression equation that best models the data is:

\[
y = 0.286x + 51.143
\]

This equation represents the linear trend of the temperature data over the months from March to October.

Would you like more details or have any further questions?

### Related Questions
1. How would the regression equation change if we included data from November to February?
2. What is the correlation coefficient for this data, and what does it imply?
3. How can we predict the temperature for November using this regression model?
4. How does the model accuracy change if we use a quadratic regression instead of linear?
5. What is the significance of the slope and intercept in this context?

### Tip
Always check the residuals (the differences between observed and predicted values) to assess how well a regression model fits the data.

Explore how to plot and analyze the average monthly temperature data from March to October in a city. Learn to find the regression equation that best fits the data using linear regression techniques. Suitable for high school students studying statistics and data analysis.

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