The table below shows the average temperature in a particular city for the months of March through October. Let x = 3 represent March, x = 4 represent April, and so on. Plot the points and then find a regression equation that best models the data. March 64 April 61 May 56 June 51 July 49 August September October 50 52 56

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### Average Monthly Temperatures in a City (March - October)

The table below shows the average temperature in a particular city for the months of March through October.

| Month     | March | April | May | June | July | August | September | October |
|-----------|-------|-------|-----|------|------|--------|-----------|---------|
| Temperature (°F) | 64    | 61    | 56  | 51   | 49   | 50     | 52        | 56      |

Here, the months are represented numerically for simplicity:
- **x = 3**: March
- **x = 4**: April
- **x = 5**: May
- **x = 6**: June
- **x = 7**: July
- **x = 8**: August
- **x = 9**: September
- **x = 10**: October

### Instructions:
1. **Plot the Points**:
   - Create a scatter plot with the month on the x-axis and the temperature on the y-axis.
   - The x-coordinates will be 3, 4, 5, 6, 7, 8, 9, and 10, corresponding to the months March to October.
   - The y-coordinates will be the average temperatures: 64, 61, 56, 51, 49, 50, 52, and 56.

2. **Find a Regression Equation**:
   - Use a statistical method such as the least squares approach to determine the best-fit regression line for the data.
   - The regression equation will model the relationship between the month (x) and the average temperature (y).

### Example Calculations:
- These calculations will provide insight into trends in temperature changes throughout the year and help predict future temperatures based on historical data.

Remember to include accurate titles and labels on your graphs for clarity. The regression equation can be instrumental in assessing whether the temperatures follow a linear trend or if another type of model might better fit the data.
Transcribed Image Text:### Average Monthly Temperatures in a City (March - October) The table below shows the average temperature in a particular city for the months of March through October. | Month | March | April | May | June | July | August | September | October | |-----------|-------|-------|-----|------|------|--------|-----------|---------| | Temperature (°F) | 64 | 61 | 56 | 51 | 49 | 50 | 52 | 56 | Here, the months are represented numerically for simplicity: - **x = 3**: March - **x = 4**: April - **x = 5**: May - **x = 6**: June - **x = 7**: July - **x = 8**: August - **x = 9**: September - **x = 10**: October ### Instructions: 1. **Plot the Points**: - Create a scatter plot with the month on the x-axis and the temperature on the y-axis. - The x-coordinates will be 3, 4, 5, 6, 7, 8, 9, and 10, corresponding to the months March to October. - The y-coordinates will be the average temperatures: 64, 61, 56, 51, 49, 50, 52, and 56. 2. **Find a Regression Equation**: - Use a statistical method such as the least squares approach to determine the best-fit regression line for the data. - The regression equation will model the relationship between the month (x) and the average temperature (y). ### Example Calculations: - These calculations will provide insight into trends in temperature changes throughout the year and help predict future temperatures based on historical data. Remember to include accurate titles and labels on your graphs for clarity. The regression equation can be instrumental in assessing whether the temperatures follow a linear trend or if another type of model might better fit the data.
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