TP: To review Standard Deviation, Residual Plots, and Correlation Coefficients HW: Do a journal entry on each of the calculator tricks in this lesson. Lesson slides will be posted with notes. Do Now: Write down the 5 statistic summary for each box plot below. Which plot has the higher interquartile range? Which box plot shows more variability? A B
Reminder: Univariate Data Example: Puppy Weights Bivariate Data You weigh the pups and get these results: 2.5, 3.5, 3.3, 3.1, 2.6, 3.6, 2.4
One of the ways we can compare univariate data is to consider Standard Deviation. Standard Deviation tells us about variability. The higher the SD, the more spread out the data is. The lower the SD, the closer together the data is.
Without calculating it, which one of these has the highest Standard Deviation? Test Scores for Class A: 68, 90, 99, 88, 41, 78 Test Scores for Class B: 87, 89, 87, 79, 84, 82
Check the website tonight for a video reminder of how to calculate standard deviation by hand. To calculate SD by calculator: 1) Enter your univariate data in L1 (Stat, Edit) 2) Go to Stat, Calc, and Select 1-Var Stats 3) "Sx" tells us standard deviation
The "correlation coefficient" of bivariate data measures the strength and type of correlation between two variables. This number is between -1 and 1. CC close to 1 or close to -1 would indicate that data is linear. CC close to 0 indicate that the data is non-linear.
Estimate whether the correlation coefficient will be closer to -1, 0 or 1. June 02, 2015
Graphing Calculator Instructions: 1. Enter your lists into L1 and L2. Use L1 for x and L2 for y. *make sure ordered pairs are together* 2. Turn "Diagnostic On" by pressing 2nd --> 0 and finding "Diagnostic On". Then, press Enter. Make sure you see the word "Done". 3. Run a regression analysis. (Stat Calc 4) *make sure the "XList" is L1 and the "YList" is L2. Press Calculate. 4. The value of "r" is the correlation coefficient (note: this test also shows you the slope and y-intercept of the line of best fit).
We can also use residual plots to determine if a line of best fit is a good representation of data. Which set of data is better modeled by the line of best fit?
To calculate residuals, create a table, the first two columns show experimental data. To find predicted value, use "LinReg" on the calculator to find the line of best fit. Then plug in each x variable and find y. The residual is the predicted value - experimental value. Line of best fit: y = 53x + 1514 Predicted value for 14 minutes: y = 53(14) + 1514 y = 2,256 Residual for 14: 2256-1510 = 746 Try the rest of the table.
To create a residual plot, make a scatter plot. The x-axis will represent the independent variable. The y-axis represents the residuals. Residuals 6 5 4 3 2 1 0-1 -2-3 -4-5 -6 25 26 27 28 29 30 31 32 33 (x) Curb weight (x)
A residual plot will describe how far away each piece of experimental data is from the predicted data. A residual plot with no pattern (some dots above the line, some below) indicates that the original data is linear. A residual plot that is curved or includes a pattern is not linear.
Which residual plot(s) describe linear data? June 02, 2015
1 Which of these cannot be used to help determine if bivariate data can be accurately described with a linear model. A Residual Plot B Standard Deviation C Correlation Coefficient D Line of Best Fit
Find the standard deviation for the following data. Then determine which is more spread out. Puppy weights A) 2.5, 4, 2.8, 3.6, 4.3 B) 1.7, 1.9, 2.0, 2.4, 4.1
Which of the following data sets would have a correlation coefficient closest to -1? 1) 2) 3) 4)
Find the equation of the line of best fit for the following data. Then use that to predict the distance traveled when the time is 148 minutes.
Fred draws two conclusions from this residual plot. First he says that this data is not linear. Second, he says that it must be quadratic because the data looks like a parabola. Which of Fred's conclusions is correct and what is wrong with the other conclusion?
Write down in your notebooks your best explanation of why data that is linear will result in a residual plot that has no pattern. Then discuss your answer with your table.
1) What would a data set with a standard deviation of 0 look like? 2) What could the correlation coefficient of a data set that is perfectly linear be? 3) What would the residual plot of a data set that is perfectly linear look like?
Summary: What does standard deviation tell us about univariate data? What do Correlation Coefficients and Residual Plots tell us about bivariate data?