Trend Trackers Worksheet SliceHeaderFix Trend Trackers Lab
Investigating Linear Relationships & Correlation
TEKS: A.4(A-C)
Date: ____________
Student: ____________
Period: ____________
TIER 1
Pattern Recognition
Mini Lesson: Reading Trends
Direction: Up from left-to-right is Positive. Down is Negative.
Strength: Dots close to a line = Strong. Dots scattered = Weak.
1.1 Label each scatter plot (Positive, Negative, or No) and estimate strength (Strong or Weak).
Direction
Strength
Direction
Strength
Direction
Strength
1.2 Association vs. Causation
Definition: Association means things happen at the same time. Causation means one thing directly creates the other result.
Circle the correct relationship for each real-world scenario.
A. As the temperature outside increases, the sales of air conditioners also increase.
Association
Causation
B. Positive correlation between the number of city libraries and city fitness centers.
Association
Causation
TIER 2
Data Modeling
Mini Lesson: Tech Analysis
Correlation Coefficient (r): Near 1 or -1 is strong. Near 0 is weak.
Linear Regression: Finding the equation \(y = ax + b\) that best fits the data using technology.
2.1 Smartphone Battery Life
Age (Months) (\(x\)) Battery % (\(y\)) 2 98 5 94 8 89 12 82 18 75 24 68
A. What is the Correlation Coefficient (\(r\))?
\(r =\) ________________
B. Describe the relationship (strength & direction).
C. Write the Linear Regression equation (\(y = ax + b\)).
\(y =\) ________________
2.2 Prediction
Based on your equation from 2.1C, what is the predicted battery percentage for a phone that is 36 months old?
Substitution & Solution
TIER 3
Expert Analysis
Mini Lesson: Context & Interpretation
Slope (m): The expected change in \(y\) for every 1 unit increase in \(x\).
Y-Intercept (b): The initial value of \(y\) when \(x\) is zero.
3.1 Contextual Interpretation
A wildlife biologist tracks the relationship between the average daily temperature in Celsius (\(x\)) and the number of chirps a cricket makes per minute (\(y\)):
\(y = 4.2x + 30.5\) | \(r = 0.94\)
A
Interpret the Slope.
Explain exactly what the number 4.2 means in terms of temperature and chirps.
B
Assess the Validity.
Is the biologist justified in using this model? Use the correlation coefficient to justify.
C
Analyze the Y-Intercept.
Identify the y-intercept and explain what it represents. Is this reasonable in real life?
© Trend Trackers Education
Algebra 1 Proficiency Tiering • A.4(A-C)
Page 3 of 3
Trend Trackers Answer Key Answer Key
Trend Trackers Lab • Teacher Resource
Confidential
Tier 1: Foundation Solutions
1.1 Scatter Plot Classification
Plot A:
Plot B:
Plot C:
1.2 Association vs. Causation
A.
Causation: Higher temperatures directly create a physical need/demand for air conditioning.
B.
Association: While cities with more libraries might have more gyms, one does not cause the other. They are likely both caused by a third factor like city size or wealth.
Tier 2: Data Modeling Solutions
2.1 Smartphone Battery Life
A. r Value: \(r \approx -0.9984\)
B. Description: Very strong negative correlation.
C. Equation: \(y = -1.37x + 100.12\)
2.2 Prediction (36 months)
\(y = -1.37(36) + 100.12\)
\(y = -49.32 + 100.12\)
Answer: 50.8%
Tier 3: Expert Analysis Solutions
A. Interpret the Slope (4.2):
"For every 1 degree Celsius increase in temperature, the cricket chirps an average of 4.2 additional times per minute."
B. Assess the Validity (\(r = 0.94\)):
"Yes, the biologist is justified. A correlation coefficient of 0.94 indicates a very strong positive linear relationship, meaning the data points are very close to the regression line."
C. Analyze the Y-Intercept (30.5):
"The y-intercept represents that at 0°C, the cricket would chirp 30.5 times per minute. This may not be reasonable in reality, as most insects become inactive or die at freezing temperatures."
Trend Trackers Lab • Answer Key • Algebra 1 • Standard A.4(A-C)
Trend Trackers Worksheet Slice Trend Trackers Lab
Investigating Linear Relationships & Correlation
TEKS: A.4(A), A.4(B), A.4(C)
Date: ________________
Student: ________________
Period: ________________
TIER 1
Pattern Recognition
Mini Lesson: Reading Trends
Direction: Look at the overall flow of the dots. If they go up from left-to-right, it's Positive. If they go down, it's Negative.
Strength: How close are the dots to forming a straight line? Close dots = Strong relationship. Scattered dots = Weak.
1.1 Label each scatter plot as Positive, Negative, or No Correlation. Then, estimate if the relationship is Strong or Weak.
Direction:
Strength:
Direction:
Strength:
Direction:
Strength:
1.2 Association vs. Causation
Note: Association means variables move together. Causation means one thing directly causes the other.
Determine if each statement describes Association or Causation.
A. As the temperature outside increases, the sales of air conditioners also increase.
Association
Causation
B. There is a positive correlation between the number of libraries in a city and the number of fitness centers.
Association
Causation
TIER 2
Data Modeling
Mini Lesson: Tech Analysis
Correlation Coefficient (r): A number from -1 to 1. Values near 1 or -1 show a strong linear trend. Values near 0 show weak or no trend.
Linear Regression: Finding the equation \(y = ax + b\) that best fits the data. We use technology to calculate this model precisely.
2.1 Smartphone Battery Life
Age (Months) (\(x\)) Battery % (\(y\)) 2 98 5 94 8 89 12 82 18 75 24 68
A. What is the Correlation Coefficient (\(r\))?
\(r =\) ________________
B. Describe the relationship (strength & direction).
C. Write the Linear Regression equation (\(y = ax + b\)).
\(y =\) ________________
2.2 Prediction
Based on your equation from 2.1C, what is the predicted battery percentage for a phone that is 36 months old?
