a) Determine the dependent (Y) and independent (X) variables.

• Independent variable (X): Temperature
  Temperature is controlled or observed as an influencing factor. It does not depend on fuel sales, but it is likely to affect them.

• Dependent variable (Y): Fuel Sold
  Fuel sold depends on temperature because as the temperature changes, the need for heating fuel varies.

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b) Draw a scatter plot to represent the data.

I'll first create the scatter plot.import matplotlib.pyplot as plt

Data

temperature = [15, 17, 18, 18, 19, 20, 21, 22, 24, 25] fuel_sold = [135, 130, 85, 50, 45, 40, 20, 25, 15, 10]

Scatter Plot

plt.figure(figsize=(8, 6)) plt.scatter(temperature, fuel_sold, marker='o', edgecolor='black') plt.title("Scatter Plot: Temperature vs Fuel Sold") plt.xlabel("Temperature (°C)") plt.ylabel("Fuel Sold (units)") plt.grid(True) plt.show() <<ImageDisplayed>>successHere is the scatter plot showing the relationship between temperature and fuel sold.

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c) Comment on the strength and direction of the linear relationship.

From the scatter plot:

• Direction: The relationship appears to be negative; as the temperature increases, fuel sales decrease.
• Strength: The points are somewhat close to a linear pattern, indicating a moderately strong negative correlation.

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d) Find the regression equation of the data.

I'll calculate the regression equation in the form $Y = a + bX$.import numpy as np from scipy.stats import linregress

Calculate the regression line

slope, intercept, r_value, p_value, std_err = linregress(temperature, fuel_sold)

Regression equation

regression_equation = f"Y = {intercept:.2f} + {slope:.2f}X"

Display results

regression_equation, r_value**2('Y = 311.69 + -12.87X', 0.7745727966156946)('Y = 311.69 + -12.87X', 0.7745727966156946)successThe regression equation for the data is:
$Y = 311.69 - 12.87X$

Where:

• $Y$: Fuel Sold
• $X$: Temperature

The $R^2$ value is approximately $0.775$, meaning about 77.5% of the variability in fuel sales is explained by the temperature.

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Interpretation of Results:

• The negative slope ($-12.87$) indicates that for each 1°C increase in temperature, the fuel sales decrease by approximately 12.87 units.
• The intercept ($311.69$) represents the estimated fuel sold when the temperature is 0°C, though this value might not be practically meaningful in this context.

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Let me know if you want a deeper explanation or further analysis!

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Expanded Questions:

1. How would the strength of the relationship be interpreted if $R^2$ was lower?
2. Could other factors besides temperature affect fuel sales? How would you model them?
3. What are the limitations of using this regression model to predict fuel sales for temperatures outside the given range?
4. How might outliers affect the regression line and $R^2$?
5. How could you test if the relationship is statistically significant?

Tip:

Always visually inspect your data with scatter plots before fitting a regression model to identify potential anomalies or nonlinear patterns.