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.