Over Lesson 4–5 5-Minute Check 1 A.positive B.negative C.no correlation The table shows the average weight for given heights. Does the data have a positive.

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Presentation transcript:

Over Lesson 4–5 5-Minute Check 1 A.positive B.negative C.no correlation The table shows the average weight for given heights. Does the data have a positive or negative correlation?

Over Lesson 4–5 5-Minute Check 2 A.140 lbs B.152 lbs C.160 lbs D.170 lbs The table shows the average weight for given heights. Approximately how much would you expect a person who is 5’6” tall to weigh?

Over Lesson 4–5 5-Minute Check 4 Refer to the scatter plot of Jessica’s visits to the park. Predict the number of times Jessica will go to the park when the temperature is 50 degrees. A.9 B.7 C.5 D.4

Vocabulary best-fit line linear regression correlation coefficient Residual plot Positive Correlation (Strong and Weak) Negative Correlation (Strong and Weak)

Line of best fit: Stat -> Edit -> Enter L1 and L2 Stat ->Calc -> #4 LinReg y=ax+b is your line of best fit r is your correlation coefficient

Example 1 Best-Fit Line EARNINGS The table shows Ariana’s hourly earnings for the years 2009– Use a graphing calculator to write an equation for the best-fit line for the data. Find and interpret the correlation coefficient. Let x be the number of years since The correlation coefficient is r=.980 which means it models the data very well.

Step 1Enter the data by pressing STAT and selecting the Edit option. Let the year 2000 be represented by 0. Enter the years since 2000 into List 1 (L 1 ). These will represent the x-values. Enter the cost into List 2 (L 2 ). These will represent the y-values. Step 2Perform the regression by pressing STAT and selecting the CALC option. Scroll down to LinReg (ax + b) and press ENTER twice. Step 3 Write the equation of the regression line by rounding the a and b values on the screen. The form we chose for the regression was ax + b, so the equation is y = 1.21x The correlation coefficient is about , which means that the equation models the data very well. *To turn on correlation coefficient, press 2 nd and 0. Find “diagnostics on” and press enter. Once it says “done” you will be able to use it. Correlation coefficient is r.

Example 1 A.y = 0.85x ; B.y = 0.95x ; C.y = 1.53x ; D.y = 1.95x ; BIOLOGY The table shows the average body temperature in degrees Celsius of nine insects at a given temperature. Use a graphing calculator to write the equation for the best-fit line for that data. Name the correlation coefficient.

Graph and Analyze a Residual Plot COST Graph and analyze the residual plot for the data comparing the years since 2010 and the cost of repairs. The plot appears to have a curved pattern, so the regression line may not fit the data well.

Graph and Analyze a Residual Plot Answer: The plot appears to have a curved pattern, so the regression line may not fit the data well. Turn on Plot1 under the STAT PLOT menu and choose Use L 1 for the Xlist and RESID for the Ylist. You can obtain RESID by pressing 2nd [STAT] and selecting RESID from the list of names. Graph the scatter plot of the residuals by pressing ZOOM and choosing ZoomStat.

Example 2 Use Interpolation and Extrapolation BOWLING The table shows the points earned by the top ten bowlers in a tournament. How many points did the 15th-ranked bowler earn? Use a graphing calculator to write an equation of the best-fit line for the data. Then extrapolate to find the missing value. Answer: The 15th-ranked player earned about 83 points.

Example 2 Use Interpolation and Extrapolation Step 2Perform the linear regression using the data in the lists. Find the equation of the best-fit line. The equation of the best-fit line is y = –7.87x Step 3Graph the best-fit line. Then use the TRACE feature and the arrow keys until you find a point where x = 15. When x = 15, y ≈ 83. Answer: The 15th-ranked player earned about 83 points. Step 1Enter the data from the table in the lists. Let the rank be the x-values and the score be the y-values. Then graph the scatter plot.

Example 2 A.1186 passengers B.1702 passengers C.1890 passengers D.2186 passengers TRAVEL An air taxi keeps track of how many passengers it carries to various islands. The table shows the number of passengers who have traveled to Kelley’s Island in previous years. How many passengers should the airline expect to go to Kelley’s Island in 2015?