Introductory StatisticsMathematics and Statistics
Regression (Fuel Efficiency)
- The student will calculate and construct the line of best fit between two variables.
- The student will evaluate the relationship between two variables to determine if that relationship is significant.
Collect the DataUse the most recent April issue of Consumer Reports. It will give the total fuel efficiency (in miles per gallon) and weight (in pounds) of new model cars with automatic transmissions. We will use this data to determine the relationship, if any, between the fuel efficiency of a car and its weight.
- Using your random number generator, randomly select 20 cars from the list and record their
weights and fuel efficiency into [link].
Weight Fuel Efficiency
- Which variable should be the dependent variable and which should be the independent variable? Why?
- By hand, do a scatterplot of “weight” vs. “fuel efficiency”. Plot the points on graph paper. Label both axes with words. Scale both axes accurately.
Analyze the Data Enter your data into your calculator or computer. Write the linear equation, rounding to 4 decimal places.
- Calculate the following:
- a = ______
- b = ______
- correlation = ______
- n = ______
- equation: ŷ = ______
- Obtain the graph of the regression line on your calculator. Sketch the regression line on the same axes as your scatter plot.
- Is the correlation significant? Explain how you determined this in complete sentences.
- Is the relationship a positive one or a negative one? Explain how you can tell and what this means in terms of weight and fuel efficiency.
- In one or two complete sentences, what is the practical interpretation of the slope of the least squares line in terms of fuel efficiency and weight?
- For a car that weighs 4,000 pounds, predict its fuel efficiency. Include units.
- Can we predict the fuel efficiency of a car that weighs 10,000 pounds using the least squares line? Explain why or why not.
- Answer each question in complete sentences.
- Does the line seem to fit the data? Why or why not?
- What does the correlation imply about the relationship between fuel efficiency and weight of a car? Is this what you expected?
- Are there any outliers? If so, which point is an outlier?
- Introductory Statistics
- Sampling and Data
- Descriptive Statistics
- Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs
- Histograms, Frequency Polygons, and Time Series Graphs
- Measures of the Location of the Data
- Box Plots
- Measures of the Center of the Data
- Skewness and the Mean, Median, and Mode
- Measures of the Spread of the Data
- Descriptive Statistics
- Probability Topics
- Discrete Random Variables
- Probability Distribution Function (PDF) for a Discrete Random Variable
- Mean or Expected Value and Standard Deviation
- Binomial Distribution
- Geometric Distribution
- Hypergeometric Distribution
- Poisson Distribution
- Discrete Distribution (Playing Card Experiment)
- Discrete Distribution (Lucky Dice Experiment)
- Continuous Random Variables
- The Normal Distribution
- The Central Limit Theorem
- Confidence Intervals
- Hypothesis Testing with One Sample
- Hypothesis Testing with Two Samples
- The Chi-Square Distribution
- Linear Regression and Correlation
- F Distribution and One-Way ANOVA
- Appendix A: Review Exercises (Ch 3-13)
- Appendix B: Practice Tests (1-4) and Final Exams
- Appendix C: Data Sets
- Appendix D: Group and Partner Projects
- Appendix E: Solution Sheets
- Appendix F: Mathematical Phrases, Symbols, and Formulas
- Appendix G: Notes for the TI-83, 83+, 84, 84+ Calculators
- Appendix H: Tables