Section 4.2 How Can We Define the Relationship between two

Slides:

Advertisements

Similar presentations

1.5 Scatter Plots and Least Squares Lines

Advertisements

Least-Squares Regression Section 3.3. Correlation measures the strength and direction of a linear relationship between two variables. How do we summarize.

Section 10-3 Regression.

Least Squares Regression

AP Statistics.  Least Squares regression is a way of finding a line that summarizes the relationship between two variables.

Objectives Fit scatter plot data using linear models with and without technology. Use linear models to make predictions.

1-4 curve fitting with linear functions

Probabilistic & Statistical Techniques Eng. Tamer Eshtawi First Semester Eng. Tamer Eshtawi First Semester

5-7: Scatter Plots & Lines of Best Fit. What is a scatter plot?  A graph in which two sets of data are plotted as ordered pairs  When looking at the.

2.4 Using Linear Models. The Trick: Converting Word Problems into Equations Warm Up: –How many ways can a $50 bill be changed into $5 and $20 bills. Work.

How Can We Describe the Relationship between two sets of Quantitative Data? 1.

Biostatistics Unit 9 – Regression and Correlation.

Researchers, such as anthropologists, are often interested in how two measurements are related. The statistical study of the relationship between variables.

Managerial Economics Demand Estimation. Scatter Diagram Regression Analysis.

Section 4.2 Least Squares Regression. Finding Linear Equation that Relates x and y values together Based on Two Points (Algebra) 1.Pick two data points.

Section 5.2: Linear Regression: Fitting a Line to Bivariate Data.

2-7 Curve Fitting with Linear Models LESSON PLAN Warm Up (Slide #2)

Correlation and Regression. Section 9.1  Correlation is a relationship between 2 variables.  Data is often represented by ordered pairs (x, y) and.

CHAPTER curve fitting with linear functions.

2-7 Curve Fitting with Linear Models Warm Up Lesson Presentation

Scatter Plots, Correlation and Linear Regression.

^ y = a + bx Stats Chapter 5 - Least Squares Regression

Statistics: Unlocking the Power of Data Lock 5 STAT 250 Dr. Kari Lock Morgan Simple Linear Regression SECTION 2.6 Least squares line Interpreting coefficients.

Section 1.6 Fitting Linear Functions to Data. Consider the set of points {(3,1), (4,3), (6,6), (8,12)} Plot these points on a graph –This is called a.

Welcome to Algebra 2! Get out your homework Get out catalogs Get out writing utensils Put bags on the floor Be quiet!!! 3/2/ : Curve Fitting with.

10.2 Regression By the end of class you will be able to graph a regression line and use it to make predictions.

Lecture 9 Sections 3.3 Objectives:

Objectives Fit scatter plot data using linear models with and without technology. Use linear models to make predictions.

Linear Regression Special Topics.

CHAPTER 3 Describing Relationships

Practice. Practice Practice Practice Practice r = X = 20 X2 = 120 Y = 19 Y2 = 123 XY = 72 N = 4 (4) 72.

Regression and Correlation

Welcome to . Week 12 Thurs . MAT135 Statistics.

Lines of Best Fit When data show a correlation, you can estimate and draw a line of best fit that approximates a trend for a set of data and use it to.

2.5 Scatter Plots & Lines of Regression

Scatter Plots Line of Best Fit

Chapter 5 LSRL.

LSRL Least Squares Regression Line

Section 13.7 Linear Correlation and Regression

Journal Heidi asked 4 people their height and shoe size. Below are the results. 63 inches inches inches inches 8 She concluded that.

4.4 Scatter Plots.

Lesson 5.3 How do you write linear equations in point-slope form?

AP Stats: 3.3 Least-Squares Regression Line

Objective The student will be able to:

LEAST – SQUARES REGRESSION

Correlation and Regression

Least-Squares Regression

^ y = a + bx Stats Chapter 5 - Least Squares Regression

Scatter Plots Line of Best Fit

Scatter Plots and Best-Fit Lines

Section 2: Linear Regression.

Comparing Linear, Exponential, and Quadratic Functions.

Chapter 5 LSRL.

Scatter Plots and Line of Best Fit

Least-Squares Regression

11C Line of Best Fit By Eye, 11D Linear Regression

Objectives Vocabulary

Section 3.2: Least Squares Regressions

Sleeping and Happiness

Lesson 2.2 Linear Regression.

Lines of Best Fit A line of best fit is a line that comes close to all the points on a scatter plot. Try to draw the line so that about the same number.

SECTION 6.2 Linear Regression

Linear Models We will determine and use linear models, and use correlation coefficients.

Section 1.3 Modeling with Linear Functions

9/27/ A Least-Squares Regression.

Warm-Up 4 minutes Graph each point in the same coordinate plane.

Homework: PG. 204 #30, 31 pg. 212 #35,36 30.) a. Reading scores are predicted to increase by for each one-point increase in IQ. For x=90: 45.98;

Presentation transcript:

Section 4.2 How Can We Define the Relationship between two sets of Quantitative Data?

Consider the Relationship Between Length and Weight in some Lengths of Channel Iron:

Scatter Plot

Find an Equation by Hand: Pick two points that define a line of best fit (the points do not have to be part of the data) … how about (19,160) & (56,518) y = mx + b ( slope = m = 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 ) … so m = 518−160 56−19 ≈9.68 Find b by plugging in the slope and one of the two points … 160 = 9.68(19) + b … so b = -23.92 So y = 9.68x – 23.92 models the relation ship between length (x) and weight (y) What do m & b represent in the data beyond slope and y-intercept?

Use the Equation: How much will a 72 length of channel weigh? y = 9.68(72) – 23.92 ≈ 673 lbs. How long would a length of channel be weighing 250 lbs.? 250 = 9.68x – 23.92, x ≈ 28.3 ft.

Least Squares Regression: A least squares regression line minimizes the sum of the squared vertical distance between the observed and predicted value. We name it 𝑦 , pronounced (y – hat) 𝑦 = mx + b … where m = r ∙ 𝑠 𝑦 𝑠 𝑥 & b = 𝑦 −𝑚 𝑥 𝑥 = 35.8 & Sx = 15.1888 𝑦 = 319.6 & Sy = 151.4754 r = .998 𝑦 = mx + b … where m = 9.953 & b = -36.72

Three Cheers for Technology: Stat … Calc … LinReg ( ax + b ) Shazaam! … 𝑦 = 9.956x – 36.833 Why is there a difference in the values from doing it by hand? What is the correlation coefficient (r – value)? r ≈ .998 Web link to a good graphing calculator regression tutorial youtube: http://www.youtube.com/watch?v=nw6GOUtC2jY

Temp/Elevation Correlation: Temperature 1542 ft 74 F 2238 ft 73 F 5426 ft 70 F 8634 ft 58 F Find 𝑦 and its correlation coefficient Graph the data and the line of best fit ( 𝑦 ) on your calculator Estimate the temperature on the top of Mt. Shasta … elevation 14,179 ft. Estimate the elevation if the temperature is 40 degrees.