Trend Trackers Handout
Linear Regression
Unit 1, Lesson 1.5
NAME:
DATE:
Your Mission
Below is a realistic, moderately scattered dataset of Study Hours vs. Quiz Scores.
| Study Hours (\(x\)) | Quiz Score (\(y\)) |
|---|
| 1.0 | 55 |
| 1.5 | 80 |
| 3.0 | 65 |
| 3.5 | 85 |
| 5.0 | 75 |
| 6.0 | 95 |
Use a straightedge (like a ruler or edge of a folder) to draw a single straight line that you feel best fits the trend of the 6 data points.
Est. y-intercept (\(b\)):
Slope sign (Pos/Neg):
Visual Scatter Plot Grid
(1,55)
(1.5,80)
(3,65)
(3.5,85)
(5,75)
(6,95)
100 90 80 70 60 50
Quiz Score
0 1 2 3 4 5 6
Study Hours
Two methods for calculation
TI-84 Plus Calculator
Hardware
- 1. DiagnosticOn (Crucial!)
Press 2nd → 0 (Catalog). Scroll to DiagnosticOn. Press ENTER twice.
- 2. Enter Your Data
Press STAT → 1: Edit.... Enter \(x\) values in L1, \(y\) values in L2.
- 3. Run Linear Regression
Press STAT → CALC → select 4: LinReg(ax+b) → scroll to Calculate → ENTER.
Desmos Graphing App
Digital
-
1. Insert a Table
Click plus icon + in top left → select Table. Input values into the columns labeled x₁ and y₁.
-
2. Request the Regression Model
In a blank formula line below the table, type exactly:
y₁ ~ m x₁ + b
Note: Use the tilde ~ key (next to the number 1 key).
-
3. Read Parameters & Stats
Read slope m and intercept b under Parameters, and correlation r under Statistics.
DATA SET
YOUR CALCULATED RESULTS
Regression Equation:
\(\hat{y} =\) \(x\ + \)
Slope (\(m\)):
y-Intercept (\(b\)):
\(r\)-Value:
Direction:
Positive Negative
Strength:
Strong Weak
Tip: Real regression lines are calculated mathematically to minimize squared distances, but your hand-drawn line should be extremely close!
Linear Regression
Unit 1, Lesson 1.5
NAME:
DATE:
Practice Mission: Complete both real-world scenarios below using your TI-84 or Desmos. Enter the datasets, compute the values, and write out your results in the requested order.
Problem #1
Screen Time vs. Quiz Scores
| Screen Time (\(x\), hrs) | Quiz Score (\(y\), %) |
|---|
| 1.5 | 92 |
| 3.0 | 85 |
| 4.5 | 78 |
| 6.0 | 68 |
| 7.5 | 60 |
Equation (\(y = mx + b\)):
y-Intercept (\(b\)):
Slope (\(m\)):
\(r\)-value:
Problem #2
Sleep Hours vs. Quiz Scores
| Sleep Time (\(x\), hrs) | Quiz Score (\(y\), %) |
|---|
| 5.0 | 65 |
| 6.5 | 78 |
| 7.0 | 84 |
| 8.0 | 92 |
| 8.5 | 95 |
Equation (\(y = mx + b\)):
y-Intercept (\(b\)):
Slope (\(m\)):
\(r\)-value:
■ What is the Correlation Coefficient?
The variable r is called the correlation coefficient. It is a single numeric value between \(-1\) and \(1\) that measures both the direction and strength of a linear relationship between two variables.
The Correlation Coefficient Scale:
-1.0 | -0.5 | 0.0 | +0.5 | +1.0
Strong Negative Weak Negative No Trend Weak Positive Strong Positive
1. The Sign (Positive or Negative)
Tells you the direction of the slope. A negative coefficient means \(y\) decreases as \(x\) increases. A positive coefficient means \(y\) increases as \(x\) increases.
2. The Size (Strength)
Tells you the strength of the relationship. The closer \(r\) is to the extreme ends (\(1\) or \(-1\)), the tighter the data points cluster around the line.
