Presentation on theme: "Linear Statistical Model"— Presentation transcript:
1Linear Statistical Model MAFS.8.SP.1.3: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.
2Mathematics Practices MP.4 Model with mathematics. Students model relationships between variables using linear and nonlinear functions. They interpret models in the context of the data and reflect on whether or not the models make sense based on slopes, initial values, or the fit to the data.MP.6 Attend to precision. Students evaluate functions to model a relationship between numerical variables. They evaluate the function by assessing the closeness of the data points to the line. They use care in interpreting the slope and the 𝑦-intercept in linear functions.MP.7 Look for and make use of structure. Students identify pattern or structure in scatter plots. They fit lines to data displayed in a scatter plot and determine the equations of lines based on points or the slope and initial value.
3Essential QuestionsHow can I use equation models to solve statistics problems?How can I interpret the slope and intercept of a data set?
4Bell-Ringer What is correlation? When one event causes another. Plotted pointsThe description of the relationship between two variables.None of the aboveWhat is a line of best fit?A break line that is vertical on the graph.The x-axis line of the data.An equation that predicts the y variable.What does it mean to make a prediction? Write your answer.
5Vocabulary Bivariate data Positive Correlation Negative Correlation In statistics, bivariate data is data that has two variables. The quantities from these two variables are often represented using a scatter plot. This is done so that the relationship (if any) between the variables is easily seen.Positive CorrelationIs when the variables of the data increases together; the correlation coefficient is between 0 and +1.Negative CorrelationIs when one variable decreases as the other increases.
7Guided PracticeThe 2014 NBA Championship Series featured the San Antonio Spurs versus the Miami Heat. The following graph compares the number of minutes each team’s starters played in game one of the championship series compared with the number of points he scored during the game.
8Guided Practice- Line of Best Fit continued Is there a correlation between the number of minutes played and the total number of points scored? Explain your answer.Draw what you think is the best fit line.a. Is there a correlation between the number of minutes a starter played and the total number of points scored by the players? Explain your answer.Answer: Yes, the more minutes they played, the more they scored.Draw a best fit line that passes through the center of the data points in the scatter plot. Answer: Approximately ½ of the data points will be above the line and ½ of the data points will be below the line. This is called the best fit line.
9Guided Practice - continues Equation of the Line of Best Fit What is the equation of the best fit line?What does the slope of the best fit line tells you about the data?Answers: a. What is the equation of the best fit line? Answer: y = x –b. What does the slope of the best fit line represent? Answer: The slope of the best fit line represents the average number of points per minute for the game.
10Guided Practice continued Answers: a. What is the intercept of the data set? Answer: 0.5If a player played 45 minutes in the game will they score more that 10 points? Answer: Yes. To make a prediction the student need to plug in/substitute 45 minutes for x into the equation of the line. Y= (45) –Y= 22 pointsWhat is the intercept of the data set?Should we expect a player that played 45 minutes to score more than 10 points? Justify your answer.
11Guided Practice solution The equation of the line of best fit. Y = x –
12Check your progressThe table below shows the test scores for individual students and the number of minutes that student spent studying for the test.Construct a scatter plot of the data. Then draw a line that seems to best represent the data.Study Time (minutes)1535204550603040Test Score (points)76858293971008991Teachers should provide graph paper to the students.
13Check your progressSketch a line of best fit through your scatter plot.Find the equation of the line of best fit.What does the slope of the best fit line tell you about the data?What, if anything, does the y-intercept tell you about the data?Use the line of best fit to predict the test score for a student who studied 25 minutes.
14The equation that we wrote is in slope – intercept form… What is the equation of the best fit line?y = xThe equation that we wrote is in slope – intercept form…Study Time (Minutes)Test ScoresStudy Time Vs. Test Scores102030405060708090100110yb represents the y-interceptm represents the slopeIs the slope positive, negative, or zero?xpositive
15Study Time Vs. Test Scores Calculations Step 1: Find the slope of the best fit lineSelect two points on the best fit line (X1,Y1) and (X2,Y2)For example (40,91) and (15,76)Use the slope formula to find the slopeM = 𝑌 𝑌 1𝑋 𝑋 1M = – 76 = = 0.640 –Show the students step by how to draw the best fit line, write the equation, make a prediction, etc.
16Study Time Vs. Test Scores Calculations Step 2: Find the y-intercept of the best fit line.Extend the best fit line to see where it crosses the y-axis.
17Study Time Vs. Test Scores Study Time Vs. Test Scores CalculationsStudy Time (Minutes)Test ScoresStudy Time Vs. Test Scores102030405060708090100110yStep 2: Find the y-intercept of the best fit line.Extend the best fit line to see where it crosses the y-axis.The y-intercept is 70.In this lesson, the y-intercept does not have an effect on the best fit line other than finding the equation of the line.x
18Study Time Vs. Test Scores Calculations Step 3: Find the equation of the best fit lineUsing the slope and y-intercept of the best fit line to find the equation in slope intercept form.y = mx + bWhere slope, m = 0.6 and y-intercept, b = 70y = 0.6x + 70Show the students step by how to draw the best fit line, write the equation, make a prediction, etc.The teacher should point out that the calculated equation of the best fit line is close to the actual equation generated by the graphing calculator or software
19Independent Classwork Part A: Organize into groups of six students. Using a tape measure, measure and record each group member’s height and arm length. Using the collected data, create a scatter plot comparing height and arm length. Sketch an approximate of the best fit line. Find the slope of the best fit line. Answer the questions attached to this worksheet. Questions: 1. What was the slope of the best fit line? 2. In terms of data (arm length and height), explain what the slope means. 3. In terms of arm length and height, what does the best fit line tell you? 4. What do you notice about the relationship between arm length and height?.
20Independent Classwork continues Part B:Input the data into Excel Spreadsheet, Geogebra software, or a graphing calculator. Using the software:Create a scatterplotFind the line of best fitCreate a regression line and display the line of best fitDisplay the equation of the line.Compare your results with the line of best fit that you created.
21Exit TicketThe scatter plot shows the number of graduates of a computer program. What is the equation for the best fit line of the data?
22Closure Administer the Summative assessment of the content covered. Assign homework to re-enforce the content covered.Give feedback on the assessment the next time you meet with the class before you move to the next content area.