Sandahl Nelson

Correlation & Regression

Slide Duration:

Section 1: Describing Data: Graphically & Numerically
Constructing & Interpreting Graphs

37m 14s

Intro
0:00
Objectives
0:08
Categorical Data
0:26
Pie Charts
0:27
Bar Graphs
1:20
(More) Bar Graphs
2:25
Comparative
2:26
Relative Frequency
3:30
Numerical Data: Discrete
4:35
Dot Plots
4:36
Stem and Leaf Plots
6:08
Example: Stem Plot
7:55
Example: Stem Plot
7:56
Numerical Data: Continuous
9:03
Numerical Data (Continuous)
9:04
Example I: Histogram
10:57
Numerical Data: Cumulative Frequency Plots
16:49
Frequency Polygon
16:50
Ogive Plot
18:00
Describe the Distribution
19:42
SOCS: Shape, Outlier, Center, Spread
19:43
Shape
20:28
Unimodal, Bimodal, or Multimodal
20:29
Symmetric Distribution
21:48
Positively Skewed Distribution
21:30
Negatively Skewed Distribution
21:46
Example II: Describe the Distribution
22:06
Stem Plots to Compare Two Groups of Data
23:06
Stem Plots to Compare Two Groups of Data
23:06
Example III: Compare the Distribution
23:47
Example IV: Describe the Distribution of Quiz Scores
27:45
Example V: Stem Plot
29:26
Example VI: Bar Graph & Relative Frequency
30:53
Summarizing Distributions of Univariate Data

1h 7m 37s

Intro
0:00
Objectives
0:10
Measuring Center
0:42
Median
0:43
Mean
0:56
Example: Find the Median and Mean
1:59
Measuring Position
6:59
Percentiles
7:10
Quartiles
7:39
Example: Find the Quartiles
8:58
11:13
Range
11:14
IQR
11:33
Variance
11:55
13:21
Example: Find the Measures of Spread
22:09
Outliers
27:23
Outliers
27:24
Example: Outliers
29:05
Boxplots
31:44
5-number Summary
31:45
Example I: Boxplot
33:55
Describe the Distribution
44:20
SOCS: Shape, Outlier, Center, Spread
44:21
Choosing Your Measure of Center & Spread
45:16
Example II: Describe the Distribution
46:08
The Effect of Changing Units on Summary Measures
48:26
Linear Transformations
48:27
Example: Distribution of Ages
50:42
Example III: Modified Boxplot & Describe the Distribution
53:26
Example IV: Describe the Distribution
1:02:37
Section 2: Correlation & Regression
Correlation & Regression

50m 16s

Intro
0:00
Objectives
0:07
Scatterplots
0:30
Scatterplots
0:31
Interpreting Scatterplots
2:20
Direction
2:34
Form
2:50
Strength
3:29
Example: Describe the Direction, Form, and Strength of the Scatterplot
4:00
Correlation Coefficient ( r )
5:22
Correlation Coefficient ( r )
5:23
Example: Correlation Coefficient ( r )
7:52
Approximate the Correlation Coefficient
7:53
Interpret the Correlation Coefficient
8:48
Least Squares Regression Line (LSRL)
9:23
Least Squares Regression Line (LSRL)
9:24
Interpreting the LSRL
10:45
y-intercept, Slope, Mean, and SD
10:46
Example: Interpreting the LSRL
14:48
Step 1: Determine the Least-squares Regression Line
14:49
Step 2: Interpret the Slope and y-intercept of the Regression Line
18:28
Step 3: Interpret the Correlation
20:56
Coefficient of Determination
23:50
R² = (r)²
23:51
Residuals
26:04
Residual = Observed y - Predicted y
26:05
Residual Plot
27:04
Example: Calculate the Residual
28:33
Example: Draw the Residual Plot
31:18
Example I: Explanatory Variable & Response Variable
37:47
Example II: Find the Least-squares Regression Line
39:08
Example III: Calculate the Residual
44:10
Example IV: Predicted Value
47:50
Example V: Residual Value
49:28
Regression, Part II

23m 26s

Intro
0:00
Objectives
0:10
Outliers and Influential Points
0:20
An OUTLIER
0:21
Influential Observations
1:05
Transformations to Achieve Linearity
2:39
Transformations to Achieve Linearity: When We Need It
2:40
Transformations to Achieve Linearity: How We Use It
4:41
Example I: Expected Number of Sales
7:11
Confounding
11:13
Confounding
11:14
Correlation Does NOT Prove Causation
11:55
Correlation Does NOT Prove Causation
11:56
Lurking Variables
13:06
Lurking Variables & Common Response
13:07
Confounding
14:25
Confounding
14:26
Example: Promotion to Increase Movie Sales
15:11
Example II: Causation, Confounding, or Common Response
16:26
Example III: Correlation
18:25
Example IV: Confounding & Common Response
19:50
Section 3: Surveys & Experiments
Planning & Conducting Surveys

29m 35s

Intro
0:00
Objectives
0:09
Census vs. Survey, Parameter vs. Statistics
0:28
Census vs. Survey, Parameter vs. Statistics
0:29
Characteristics of a Well-Designed and Well-Conducted Survey
2:15
Representative Sample
2:16
Random Sample
3:38
Does Not Introduce Bias
4:02
Bias
4:16
What Is It?
4:17
How Might It Occur?
5:26
Example I: Identify the Type of Bias
7:03
Random Sampling
10:25
Simple Random Sample (SRS)
10:26
Example II: Random Sampling
13:26
Random Sampling, Cont.
16:44
Stratified Random Sampling
16:55
Cluster Sample
18:06
Systematic Random Sample
19:16
Example III: Random Sampling
20:52
Non-Random Sampling
22:28
Convenience Sample
22:29
Voluntary Response Sample
22:54
Example IV: Sampling Design
25:01
Specify The Population
25:02
Describe The Sampling Design. Will You Use a Stratified Sample?
26:46
Planning & Conducting Experiments

41m 31s

Intro
0:00
Objectives
0:09
Experiments vs. Observational Studies
0:44
Observational Study
0:45
Experiment
1:28
Example I: Experimental or Observational?
2:09
Example II: Experimental or Observational?
2:57
Placebo Effect
3:51
Placebo Effect
3:52
Characteristics of a Well-designed and Well-conducted Experiment
4:42
Control
4:43
Replicate
5:32
Randomize
6:32
Example III: Control Groups
7:33
Completely Randomized Design
9:01
Completely Randomized Design
9:02
Outline/Map of Completely Randomized Design
9:55
Outline/Map of Completely Randomized Design
9:56
Example IV: Completely Randomized Design
11:35
Block Randomization
14:23
Block Randomization
14:24
Randomized Block Design
15:29
Randomized Block Design
15:30
Example V: Randomized Block Design
18:06
Matched Pairs Design
21:08
Matched Pairs Design
21:09
Example V: Types of Experiments
22:42
Example VI: Types of Experiments
24:17
Example VII: Types of Experiments
26:24
Experimental Set Up
28:28
Treatment
28:29
Experimental Units
29:13
Response
29:32
Double-blind Experiment
31:06
Double-blind Experiment
31:07
Example VIII: Double-blind Experiment
32:37
Example IX: Design a Study to Test Hypothesis
37:04
Generalizability of Results
40:39
Statistically Significant Data
40:40
Section 4: Probability & Expected Value
Probability Overview

1h 22m 17s

Intro
0:00
Objectives
0:21
Interpreting Probability
0:46
Probability of a Random Outcome or the Long Term Relative Frequency
0:47
Law of Large Numbers
1:42
Expected Value
1:43
Example I: Probability in Poker
2:21
Probability Model
4:31
Sample Space (S)
4:32
Event
5:15
Probabilities
6:03
Example II: Basketball Free Throws
6:37
Part 1: Sample Space
6:46
Part 2: Event
8:08
Part 3: Probability
8:48
Disjoin Events (aka Mutually Exclusive)
11:00
Disjoin Events (aka Mutually Exclusive)
11:01
Example III: Advertising Contracts
12:23
Part A: Venn Diagram
12:24
Probability of Disjoin Events
14:03
Probability of Disjoin Events
14:04
Example IV: Probability of Disjoin Events
15:58
Independence vs. Dependence
18:11
Independence vs. Dependence
18:12
Example V: Independence vs. Dependence
20:26
Example VI: Independence vs. Dependence
22:23
Probability Rules
23:13
Probability Rules
23:14
Probability Notation
23:31
P (A or B)
23:32
P (A and B)
23:58
P ( A given B happened)
24:24
P ( not A)
24:44
Example VII: Probability Notation
25:17
Probability Rule Notation
26:49
A or B
26:50
A and B
27:40
Example VIII: Determine if These Two Events are Independent
29:05
Example IX: Conditional Probability of Wining
31:39
Example X: Conditional Probability of Students
36:46
Part A: Probability
36:47
Part B: Conditional Probability
38:18
Part C: Conditional Probability
39:59
Example XI: Conditional Probability of Children
42:53
Part A: All Boys
42:54
Part B: All Girls
44:44
Part C: Exactly Two Boys or Exactly Two Girls
45:50
Part D: At Least One Child of Each Sex
50:18
Overview
52:52
Complement
52:53
Mutually Exclusive
53:30
Intersection
53:49
Union
54:44
Independent
55:34
Bayes Rule
56:02
Bayes Rule
56:03
Example XI: Probability & Bayes Rule
59:43
Example XII: Probability & Bayes Rule
1:07:49
Simulations
1:05:46
Simulations
1:05:47
Example XIII: Simulations
1:07:10
Intro to Probability for Discrete Random Variables

31m 37s

Intro
0:00
Objectives
0:09
Discrete vs. Continuous Random Variables
0:29
Discrete Random Variables
0:30
Continuous Random Variables
1:12
Probability Distribution
3:36
Probability Distribution for a Discrete Random Variables
3:37
Probability Rules
4:20
Example I: Find the Probability
4:51
Example II: Construct a Probability Distribution
6:15
Mean
9:35
Expected Value
9:36
Example: Expected Number of Customers
10:08
Variance
13:19
Variance
13:20
Example: Variance
14:34
Example III: Probability Analysis
18:01
Example IV: Expected Profit
25:25
Discrete Random Variables

39m 6s

Intro
0:00
Objectives
0:08
Binomial Distribution
0:14
BINP
0:15
B
0:34
I
0:49
N
1:00
P
1:20
Example I: Binomial Distribution
1:43
Question 1: Is a Binomial Distribution a Reasonable Probability Model for the Random Variable X?
1:44
Question 2: Is a Binomial Distribution a Reasonable Probability Model for the Random Variable X?
3:43
Binomial Probability
5:11
Binompdf (n, p, x)
5:12
Example II: Determine the Probability
10:37
Part A: Determine the Probability that Exactly One of the Toasters is Defective
10:38
Part B: Determine the Probability that At Most Two of the Toasters are Defective
16:40
Part C: Determine the Probability that More Than Three of the Toasters are Defective
21:42
Geometric Distribution
24:11
Geometric Distribution
24:12
Example III: Geometric Distribution & Probability
25:14
Part A: Geometric Distribution
25:15
Geometric Probability
26:55
Geometpdf (p, x)
26:56
Example III: Geometric Distribution & Probability
27:50
Part B: Geometric Probability of Exactly Four Patients
27:51
Part C: Geometric Probability of At Most Five Patients
31:19
Mean and SDs
33:47
Binomial
33:48
Geometric
34:28
Example IV: Defective Units
34:53
Example V: Number of Patients
35:58
Combining Independent Random Variables

18m 56s

Intro
0:00
Objectives
0:09
Mean and Standard Deviation of Two Random Variables
0:26
Mean and Standard Deviation of Two Random Variables
0:27
Example I: Average and Standard Deviation
1:58
Example II: Average and Standard Deviation
4:37
Transforming Random Variables: “Linear Transformations”
6:10
Transforming Random Variables: “Linear Transformations”
6:11
Example III: Mean and Standard Deviation
7:02
Example IV: Mean and Standard Deviation
10:23
Example V: Mean and Standard Deviation
14:14
Part 1: Mean & SD
14:15
Part 2: Mean & SD
16:30
Normal Random Variables

59m 34s

Intro
0:00
Objectives
0:08
The Empirical Rule
0:28
68%
0:29
95%
1:43
99.70%
2:00
The Empirical Rule, Cont.
2:31
The Empirical Rule, Cont.
2:32
Example I: The Empirical Rule
3:24
Z-Score
8:17
Z-Score
8:18
Example II: Z-Score
10:08
Using the Normal Table
13:03
Using the Normal Table
13:04
Using the Normal Table, Cont.
15:05
Example III: Using the Normal Table and Z-score to Calculate Probability
16:01
Step 1: Sketch
16:02
Step 2: Calculate Z-score
18:16
Step 3: Solve for Probability Using the Normal Table
19:14
Example IV: Using the Normal Table and Z-score to Calculate Probability
20:29
Step 1: Sketch
20:30
Step 2: Calculate Z-score
21:52
Step 3: Solve for Probability Using the Normal Table
22:36
Example V: Using the Normal Table and Z-score to Calculate Probability
27:20
Step 1: Sketch
27:42
Step 2: Calculate Z-score
28:14
Step 3: Solve for Probability Using the Normal Table
29:45
Example VI: Using the Normal Table and Z-score to Calculate Probability
34:00
Step 1: Sketch
34:01
Step 2: Calculate Z-score
35:48
Step 3: Solve for Probability Using the Normal Table
36:56
Example VII: Using the Normal Table and Z-score to Calculate Probability
41:21
Step 1: Sketch
41:22
Step 2: Calculate Z-score
44:15
Step 3: Solve for Probability Using the Normal Table
47:26
Example VIII: Calculate the Standard Deviation of the Random Normal Variable
49:54
Step 1: Sketch
49:55
Step 2: Calculate Z-score
51:16
Step 3: Solve for Standard Deviation
53:16
Example VIII: Calculate the Mean of the Distribution
55:11
Step 1: Sketch
55:12
Step 2: Calculate Z-score
56:36
Step 3: Solve for Mean
57:42
Section 6: Distribution of Data
Sampling Distributions

38m 27s

Intro
0:00
Objectives
0:07
Parameter vs. Statistics
0:25
Parameter vs. Statistics
0:26
Sampling Distribution
2:03
Sampling Distribution
2:04
Central Limit Theorem
3:15
Central Limit Theorem
3:16
Central Limit Theorem, Cont.
7:23
Example I: Sampling Distribution Graph
9:20
Conditions (RIN)
11:12
Random
11:13
Independent
12:04
Normal
13:40
Sampling Distribution of a Sample Mean
15:19
Sampling Distribution of a Sample Mean
15:20
Example II: Calculate the Mean and SD of a Sampling Distribution
17:17
Sampling Distribution of a Sample Proportion
21:07
Sampling Distribution of a Sample Proportion
21:08
Example III: Mean, SD, Sample Size, and Probability of a Sampling Distribution
22:29
Part A: Calculate the Mean and SD of a Sampling Distribution
22:30
Part B: Sample Size
26:18
Part C: Probability
29:30
Example IV: Probability of a Sampling Distribution
33:40
Part A: Probability of a Random Selection
33:41
Part B: Probability of the Mean
35:46
Section 7: Statistical Inference
Confidence Intervals

56m 37s

Intro
0:00
Lesson Overview
0:07
Why Calculate a Confidence Interval?
0:28
Using a Statistic to Estimate a Parameter
0:29
What is a Confidence Interval?
1:24
Confidence Interval
1:25
General math Behind a Confidence Interval
2:51
Point Estimate
2:52
Critical Value
4:34
Z-Table
6:06
Z-Table
6:07
T-Table
7:07
T-Table
7:08
General math Behind a Confidence Interval
7:50
Point Estimate
7:51
Critical Value: Mean & Proportion
8:00
Standard Error: Mean & Proportion
8:15
Calculating Using Your Calculator
10:46
Steps to Calculating a Confidence Interval
12:09
12:10
Step 2: Check Your Conditions
12:58
Step 3: Calculate
15:33
Step 4: Interpret
16:12
Example I: Confidence Interval
16:29
Example II: Confidence Interval
29:57
Example III: Confidence Interval
42:31
Hypothesis Testing

1h 12m 16s

Intro
0:00
Lesson Overview
0:07
Why do a Hypothesis Test?
0:29
Using a Statistic to Test a Claim about a Parameter
0:30
Steps for Calculating a Hypothesis Test
1:13
1. Write the Hypothesis
1:14
2. Check Conditions
1:30
3. Calculate the Test Statistic
1:34
4. Look Up the P-value & Interpret
1:49
5. Interpret
1:50
Example I: Hypothesis Testing Step by Step
2:57
1. Write the Hypothesis
5:04
2. Check Conditions
8:43
3. Calculate the Test Statistic
21:54
4. Look Up the P-value
20:07
5. Interpret
23:45
Example II: Hypothesis Testing Step by Step
28:49
1. Write the Hypothesis
28:50
2. Check Conditions
32:00
3. Calculate the Test Statistic
34:20
4. Look Up the P-value
38:26
5. Interpret
40:49
Example III: Hypothesis Test for a Mean
44:53
Example IV: Hypothesis Test for a Proportion
57:26
The T Distribution

41m 40s

Intro
0:00
Lesson Overview
0:07
When Do We Use the T Distribution
0:26
When Do We Use the T Distribution
0:27
What is the T Distribution?
1:46
What is the T Distribution?
1:47
Confidence Interval Example
2:49
Construct and Interpret a 90% Confidence Interval to Estimate the Mean
2:50
Hypothesis Test Example
16:59
1. Write the Hypothesis
17:00
2. Check Conditions
20:01
3. Calculate the Test Statistic
21:24
4. Look Up the P-value
24:39
5. Interpret
27:23
Matched Pairs T-test
29:34
Matched Pairs T-test
29:35
1. Write the Hypothesis
33:05
2. Check Conditions
34:58
3. Calculate the Test Statistic
35:52
4. Look Up the P-value
38:12
5. Interpret
39:28
Two Samples

1h 27m 23s

Intro
0:00
Lesson Overview
0:09
What Will a 2 Sample Problem Look Like?
0:40
Example 1
0:41
Example 2
2:01
3:36
3:37
Hypothesis Test Example I
7:02
1. Write the Hypothesis
7:03
2. Check Conditions
10:04
3. Calculate the Test Statistic
13:21
4. Look Up the P-value
20:54
5. Interpret
22:48
Hypothesis Test Example II
24:50
1. Write the Hypothesis
24:51
2. Check Conditions
28:34
3. Calculate the Test Statistic
29:46
4. Look Up the P-value
36:27
5. Interpret
39:01
Example I: Two Samples Hypothesis Testing
42:11
Example II: Two Samples Hypothesis Testing
53:30
“Pick Your Test” Map
1:10:47
“Pick Your Test” Map
1:10:48
Example III: Reliability Testing
1:18:31
Hypothesis Testing of Least-Squares Regression Line

53m 49s

Intro
0:00
Lesson Overview
0:10
Review of Least-squares Regression and Interpretation
0:29
Correlation Coefficient ( r )
0:30
Equation of the Least-squares Regression Line
1:02
Example
2:45
Part A: Least-squares Regression Line
2:46
Part B: Slope of the Least-squares Regression Line
6:03
Test for the Regression Line
7:50
Is There a Correlation?
7:51
Is the y-intercept = 0?
9:56
Conditions for Hypothesis Testing
10:49
Linearity
11:27
Constant Variability
12:35
Normality
13:40
Independence
15:16
Hypothesis Testing
16:10
Standard Deviation of the Residuals
16:11
Standard Error of Slope
17:30
Test Statistic
18:45
Confidence Interval
19:36
Example: Hypothesis Testing
20:45
Part A: Test the Hypothesis
20:46
Part B: 95% Confidence Interval of the Slope
32:51
Interpreting Computer Output
35:40
Interpreting Computer Output
35:41
Example I: Interpreting Computer Output
38:46
Part A: Least-squares Regression Equation
38:47
Part B: Standard Error
40:01
Part C: Slope of the Least-squares Regression Line
41:21
Part D: Null and Alternative Hypotheses
42:08
Part E: Value of Test Statistic
43:09
Part G: P-Value
44:03
Part H: Is Income Useful for Predicting the Cost of a Person’s Car?
45:46
Part I: Estimated Cost
46:57
Example II: Interpreting Computer Output
47:48
Hypothesis Tests for Categorical Data (Chi-Squared Tests)

1h 12m 55s

Intro
0:00
Lesson Overview
0:11
How Do We Know to Use a Chi-Squared Test?
0:27
Categorical Data
0:28
Chi-Squared Goodness of Fit Test
1:50
One Categorical Variable with Counts in Each Category
1:51
What We Have Seen
2:17
New Question Type
2:56
Example I: Chi-Squared Goodness of Fit Test
4:02
Chi-Squared Goodness of Fit Steps Overview
4:03
Step 1: Hypothesis
5:54
Step 2: Expected
7:42
Step 3: Conditions
10:34
Step 4: Calculate
11:44
Step 5: P-Value & Chi-Square Distribution Table
17:03
Example II: Chi-Squared Goodness of Fit Test
22:04
Step 1: Hypothesis
22:05
Step 2: Expected
24:55
Step 3: Calculate
29:05
Step 4: P-Value & Chi-Square Distribution Table
33:18
Chi-Squared Test of: Homogeneity or Independence/Association
34:31
Homogeneity
34:32
Independence/Association
35:42
Example III: Chi-Squared Test of: Homogeneity or Independence/Association
37:55
Step 1: Hypothesis
37:56
Step 2: Expected
40:28
Step 3: Conditions
46:48
Step 4: Calculate
47:49
Step 5: P-Value & Chi-Square Distribution Table
49:30
As a Test of Association
52:53
As a Test of Association
52:54
Example IV: Chi-Squared Test of: Homogeneity or Independence/Association
55:05
Step 1: Hypothesis, Expected, and Conditions
55:06
Step 2: Calculate
59:45
Step3: P-Value & Chi-Square Distribution Table
1:01:51
Example V: Chi-Squared Test of: Homogeneity or Independence/Association
1:02:48
Step 1: Hypothesis
1:02:49
Step 2: Expected and Conditions
1:05:12
Step 3: Calculate
1:06:36
Step 4: P-Value & Chi-Square Distribution Table
1:10:50
Section 8: AP Practice Test
Practice Test 2013 AP Statistics

1h 2m 57s

Intro
0:00
Question 1
0:23
Question 1: Part A
0:24
Question 1: Part B
2:10
Question 2
6:16
Question 2: Part A
6:17
Question 2: Part B
10:22
Question 2: Part C
12:09
Question 3
14:30
Question 3: Part A
14:31
Question 3: Part B
18:19
Question 4
24:49
Question 4: Part A
24:50
Question 5
37:27
Question 5: Part A
37:28
Question 5: Part B
42:32
Question 6
51:15
Question 6: Part A
51:16
Question 6: Part B
55:17
Practice Test 2014 AP Statistics

1h 7s

Intro
0:00
Question 1
0:32
Question 2
9:46
Question 2: Part A
9:47
Question 2: Part B
12:28
Question 2: Part C
13:22
Question 3
15:38
Question 3: Part A
15:39
Question 3: Part B
18:40
Question 4
27:33
Question 4: Part A
27:34
Question 4: Part B
30:05
Question 5
34:15
Question 5: Part 1
34:16
Question 5: Part 2
37:29
Question 5: Part 3
39:50
Question 5: Part 4
40:59
Question 5: Part 5
44:09
Question 6
45:30
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 1 answerLast reply by: Ronald ChMon Jul 27, 2020 1:43 PMPost by Tran Huy on May 6, 2018What is the difference between r and r^2? 1 answerLast reply by: Sandahl NelsonThu Mar 17, 2016 4:50 PMPost by Xiaming Jin on February 24, 2016On calculator, why we should use LinReg y=a+bx? If use ax+b, does that means just exchange the value of a and b?

### Correlation & Regression

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

• Intro 0:00
• Objectives 0:07
• Scatterplots 0:30
• Scatterplots
• Interpreting Scatterplots 2:20
• Direction
• Form
• Strength
• Example: Describe the Direction, Form, and Strength of the Scatterplot 4:00
• Correlation Coefficient ( r ) 5:22
• Correlation Coefficient ( r )
• Example: Correlation Coefficient ( r ) 7:52
• Approximate the Correlation Coefficient
• Interpret the Correlation Coefficient
• Least Squares Regression Line (LSRL) 9:23
• Least Squares Regression Line (LSRL)
• Interpreting the LSRL 10:45
• y-intercept, Slope, Mean, and SD
• Example: Interpreting the LSRL 14:48
• Step 1: Determine the Least-squares Regression Line
• Step 2: Interpret the Slope and y-intercept of the Regression Line
• Step 3: Interpret the Correlation
• Coefficient of Determination 23:50
• R² = (r)²
• Residuals 26:04
• Residual = Observed y - Predicted y
• Residual Plot
• Example: Calculate the Residual 28:33
• Example: Draw the Residual Plot 31:18
• Example I: Explanatory Variable & Response Variable 37:47
• Example II: Find the Least-squares Regression Line 39:08
• Example III: Calculate the Residual 44:10
• Example IV: Predicted Value 47:50
• Example V: Residual Value 49:28

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