trend lines and lines of best fit. statisticians gather data to determine correlations...
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ScatterplotsTrend lines and Lines of best fit
Statisticians gather data to determine correlations (relationships) between events.
Scatter plots will often show at a glance whether a relationship exists between two sets of data.
Scatterplots
Let's decide if studying longer will affect grades based upon a specific set of data. Given the data below, a scatter plot has been prepared to represent the data. Remember when making a scatter plot, do NOT connect the dots.
The data displayed on the graph resembles a line rising from left to right. Since the slope of the line is positive, there is a positive correlation between the two sets of data. This means that according to this set of data, the longer I study, the better grade I will get on my exam.
Positive Correlation
Negative Correlation
No Correlation
When data is displayed with a scatter plot, it is often useful to attempt to represent that data with the equation of a straight line for purposes of predicting values that may not be displayed on the plot.
When the equation of the line is found without the use of technology or an exact statistical process we will call it the trend line.
The trend line will differ based on the points you select.
Trend Line
When the equation of the line is found the use of technology or using a statistical process we will call it the line of best fit.
The line of best fit will be the same line for everybody.
Line of Best fit
Find the trend line
Find the trend line
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Sandwich Fat and Calories
Fat
Calo
ries
About half of data points above and half below through two of your points
Find slope(9, 260) and (31,560)
Find the trend line
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Sandwich Fat and Calories
Fat
Calo
ries
11
150
22
300
x
ym
Write the equation Find slope
(9, 260) and
Find the trend line
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Sandwich Fat and Calories
Fat
Calo
ries
11
150m
)( 11 xxmyy
)9(11
150260 xy
11
8122
11
150260 xy
Use equation to predictSandwich with 40g of fat
Find the trend line
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Sandwich Fat and Calories
Fat
Calo
ries
11
3137
11
150 xy
calories
y
19.40811
3137)40(
11
150
Type data in List
Turn scatterplot on and look at it
Find line of best fit with TI 84
Calculate line of best fit
Find line of best fit with TI 84
y=11.73 x + 193.85