To solve the problem, we need to:

1. Determine the linear regression equation for the given data, where: $y = mx + b$ Here, $y$ represents the Exam Score, $x$ represents Hours Spent Studying, $m$ is the slope, and $b$ is the y-intercept.

2. Use the equation to solve for the number of hours ($x$) that corresponds to an exam score ($y$) of 84.

Let me extract the data and calculate the regression. pandas as pd import numpy as np from sklearn.linear_model import LinearRegression

Data extracted from the table

data = { "Hours Spent Studying": [2.5, 5.1, 3.2, 8.5, 3.5, 1.5, 9.2, 5.5, 8.3, 2.7, 7.7, 5.9, 4.5, 3.3, 1.1, 8.9, 2.5, 1.9, 6.1, 7.4, 2.7, 4.8, 3.8, 6.9, 7.8], "Exam Score": [21, 47, 27, 75, 30, 20, 88, 60, 81, 25, 85, 62, 41, 42, 17, 95, 30, 24, 67, 69, 30, 54, 35, 67, 86] }

Convert the data into a DataFrame

df = pd.DataFrame(data)

Separate independent (X) and dependent (Y) variables

X = df[["Hours Spent Studying"]] y = df["Exam Score"]

Perform linear regression

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

Extract slope (m) and intercept (b)

m = model.coef_[0] b = model.intercept_

Calculate the hours required for a score of 84

target_score = 84 required_hours = (target_score - b) / m

m, b, required_hoursThe linear regression equation is:

$y = 9.665x + 2.680$

Using this equation, the number of hours a student needs to study to achieve an exam score of 84 is approximately:

$x = \frac{84 - 2.680}{9.665} \approx 8.41 \text{ hours.}$

Final Answer:

The student should study for approximately 8.41 hours.

Do you want a step-by-step explanation of the calculations?

Related Questions:

1. How is the slope of a regression line calculated from data?
2. What does the y-intercept signify in this context?
3. How does linear regression ensure the best fit for the data?
4. What are potential limitations of using a linear model here?
5. How can we calculate prediction accuracy for this model?

Tip:

Always visualize data with scatter plots before applying regression to check if linear assumptions are valid!