pandas as pd import matplotlib.pyplot as plt import numpy as np

Data from the survey

data = { "Hours Studied": [1, 3, 5, 7, 8, 10, 12, 14, 15, 17, 19, 21, 22, 24, 25], "Test Score": [35, 52, 64, 58, 67, 60, 78, 82, 74, 86, 95, 88, 94, 98, 97] }

Create a DataFrame

df = pd.DataFrame(data)

Create a scatter plot

plt.figure(figsize=(10, 6)) plt.scatter(df["Hours Studied"], df["Test Score"], color='blue', label="Data Points") plt.title("Hours Studied vs. Test Score") plt.xlabel("Hours Studied") plt.ylabel("Test Score") plt.grid(True) plt.legend() plt.show()

Linear regression (fitting the model)

from sklearn.linear_model import LinearRegression

X = np.array(df["Hours Studied"]).reshape(-1, 1) y = np.array(df["Test Score"])

model = LinearRegression() model.fit(X, y)

Model slope and intercept

slope = model.coef_[0] intercept = model.intercept_

Generate the regression line

line_x = np.linspace(min(df["Hours Studied"]), max(df["Hours Studied"]), 100) line_y = slope * line_x + intercept

Plot the regression line along with the scatter plot

plt.figure(figsize=(10, 6)) plt.scatter(df["Hours Studied"], df["Test Score"], color='blue', label="Data Points") plt.plot(line_x, line_y, color='red', label=f"Fit Line: y = {slope:.2f}x + {intercept:.2f}") plt.title("Linear Model Fit") plt.xlabel("Hours Studied") plt.ylabel("Test Score") plt.grid(True) plt.legend() plt.show()

Predictions for 4 and 20 hours of study

prediction_4 = model.predict(np.array([[4]]))[0] prediction_20 = model.predict(np.array([[20]]))[0]

Summary of results

(slope, intercept, prediction_4, prediction_20)### Results:

Slope-Intercept Form of the Model:
The equation of the linear model is:
$y = 2.31x + 43.99$
where $y$ is the test score, and $x$ is the hours studied.

Predictions:

• For 4 hours of study, the predicted test score is approximately 53.21.
• For 20 hours of study, the predicted test score is approximately 90.11.

Analysis of the Model: The positive slope ($2.31$) indicates that there is a strong positive relationship between hours studied and test scores. On average, each additional hour of studying increases the test score by approximately 2.31 points. The intercept ($43.99$) suggests that a student who doesn't study at all is expected to score approximately 44 points.

If you'd like, I can prepare a detailed report, including reflection and insights, based on these results. Let me know how you'd like to proceed or if you have further questions!

Related Questions:

1. How can this model be improved for better accuracy?
2. What could be the effect of outliers on the linear model?
3. Can other models, such as quadratic or exponential, better fit this data?
4. How reliable is this model for extreme values (e.g., 0 or 30 hours studied)?
5. What are the limitations of using a linear regression model in this scenario?

Tip:

Always consider visualizing residuals to check the goodness of fit for the chosen model.