Table of contents

1. Introduction to Statistics53m

Intro to Stats
22m

Intro to Collecting Data
8m

Sampling Methods
23m

2. Describing Data with Tables and Graphs2h 2m

Visualizing Qualitative vs. Quantitative Data
4m

Frequency Distributions
35m

Histograms
7m

Histograms w/ Graphing CalculatorBonus
13m

Bar Graphs and Pareto Charts
11m

Pie Charts
9m

Frequency Polygons
10m

Dot Plots
6m

Stemplots (Stem-and-Leaf Plots)
14m

Time-Series Graph
9m

3. Describing Data Numerically2h 8m

Mean
9m

Median
20m

Mode
7m

Standard Deviation
16m

Interpreting Standard Deviation
20m

Percentiles & Quartiles
14m

5-Number Summary Using a TI-84Bonus
10m

Boxplots
8m

Descriptive Statistics-ExcelBonus
11m

Boxplots-ExcelBonus
8m

4. Probability2h 27m

Basic Concepts of Probability
7m

Complements
6m

Addition Rule
17m

Multiplication Rule: Independent Events
11m

Introduction to Contingency Tables
17m

Multiplication Rule: Dependent Events
23m

Bayes' Theorem
13m

Fundamental Counting Principle
8m

Counting
41m

5. Binomial Distribution & Discrete Random Variables3h 28m

Discrete Random Variables
38m

Binomial Distribution
1h 17m

Finding Binomial Probabilities-ExcelBonus
17m

Poisson Distribution
45m

Finding Poisson Probabilities-ExcelBonus
15m

Hypergeometric Distribution
14m

6. Normal Distribution & Continuous Random Variables2h 21m

Uniform Distribution
19m

Standard Normal Distribution
39m

Probabilities & Z-Scores w/ Graphing CalculatorBonus
19m

Non-Standard Normal Distribution
30m

Finding Probabilities, Z Values, and X Values with the Normal Distribution-ExcelBonus
32m

7. Sampling Distributions & Confidence Intervals: Mean3h 37m

Sampling Distribution of the Sample Mean and Central Limit Theorem
19m

Distribution of Sample Mean - ExcelBonus
23m

Introduction to Confidence Intervals
22m

Confidence Intervals for Population Mean
1h 26m

Determining the Minimum Sample Size Required
12m

Finding Probabilities and T Critical Values - ExcelBonus
28m

Confidence Intervals for Population Means - ExcelBonus
25m

8. Sampling Distributions & Confidence Intervals: Proportion2h 20m

Sampling Distribution of Sample Proportion
35m

Confidence Intervals for Population Proportion
45m

Confidence Intervals for Population Proportion - ExcelBonus
12m

Chi Square Distribution
20m

Confidence Intervals for Population Variance
26m

9. Hypothesis Testing for One Sample5h 15m

Steps in Hypothesis Testing
1h 13m

Performing Hypothesis Tests: Means
1h 1m

Hypothesis Testing: Means - ExcelBonus
42m

Performing Hypothesis Tests: Proportions
39m

Hypothesis Testing: Proportions - ExcelBonus
27m

Performing Hypothesis Tests: Variance
12m

Critical Values and Rejection Regions
29m

Link Between Confidence Intervals and Hypothesis Testing
12m

Type I & Type II Errors
16m

10. Hypothesis Testing for Two Samples5h 35m

Two Proportions
1h 12m

Two Proportions Hypothesis Test - ExcelBonus
28m

Two Means - Unknown, Unequal Variance
1h 2m

Two Means - Unknown Variances Hypothesis Test - ExcelBonus
12m

Two Means - Unknown, Equal Variance
15m

Two Means - Unknown, Equal Variances Hypothesis Test - ExcelBonus
9m

Two Means - Known Variance
12m

Two Means - Sigma Known Hypothesis Test - ExcelBonus
21m

Two Means - Matched Pairs (Dependent Samples)
42m

Matched Pairs Hypothesis Test - ExcelBonus
12m

Two Variances and F Distribution
29m

Two Variances - Graphing CalculatorBonus
15m

11. Correlation1h 24m

Scatterplots & Intro to Correlation
26m

Correlation Coefficient
21m

Creating Scatterplots and FInding Correlation Coefficient - ExcelBonus
6m

Hypothesis Tests for Correlation Coefficient Using TI-85Bonus
17m

Inferences for the Correlation Coefficient - ExcelBonus
11m

12. Regression3h 42m

Linear Regression & Least Squares Method
26m

Residuals
12m

Coefficient of Determination
12m

Regression Line Equation and Coefficient of Determination - ExcelBonus
8m

Finding Residuals and Creating Residual Plots - ExcelBonus
11m

Inferences for Slope
32m

Enabling Data Analysis ToolpakBonus
1m

Regression Readout of the Data Analysis Toolpak - ExcelBonus
21m

Prediction Intervals
13m

Prediction Intervals - ExcelBonus
19m

Multiple Regression - ExcelBonus
29m

Quadratic Regression
23m

Quadratic Regression - ExcelBonus
10m

13. Chi-Square Tests & Goodness of Fit2h 31m

Goodness of Fit Test
50m

Goodness of FIt Test Using TI-84Bonus
18m

Goodness of Fit Test - ExcelBonus
10m

Contingency Tables
13m

Independence Tests
14m

Homogeneity Tests
11m

Using Matrices on a TI-84Bonus
6m

Independence Test Using TI-84Bonus
12m

Independence Tests - ExcelBonus
13m

14. ANOVA2h 33m

Introduction to ANOVA
35m

One-Way ANOVA - ExcelBonus
12m

Multiple Comparisons: Tukey Test
14m

Multiple Comparisons: Tukey-Kramer Test
15m

Multiple Comparisons: Bonferoni Test
24m

Two-Way ANOVA
32m

Two-Way ANOVA - ExcelBonus
18m

12. Regression

Coefficient of Determination

Statistics for Business

12. Regression

Coefficient of Determination

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Multiple Choice

In a given dataset, you determine the value of the correlation coefficient to be $r=-0.957$ . Find the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? What about the unexplained variation?

Explained = 91.6%; Unexplained = 8.4%

Explained = 95.7%; Unexplained = 4.3%

Explained = 8.4%; Unexplained = 91.6%

Explained = 4.3%; Unexplained = 95.7%

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Verified step by step guidance

Step 1: Recall the formula for the coefficient of determination (R²), which is the square of the correlation coefficient (r). Mathematically, R² = r².

Step 2: Substitute the given value of r into the formula. Here, r = -0.957, so calculate R² = (-0.957)².

Step 3: Interpret the coefficient of determination (R²). It represents the proportion of the variation in the dependent variable that is explained by the independent variable(s) in the regression model.

Step 4: To find the explained variation, multiply R² by 100 to express it as a percentage. This percentage indicates how much of the total variation in the data is explained by the regression line.

Step 5: To find the unexplained variation, subtract the explained variation percentage from 100%. This represents the proportion of the variation in the data that is not explained by the regression line.