Modeling relationships with a line
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Modeling Relationships with a Line. Math Notebook. Line of Best Fit. A  line of best fit   (or " trend " line) is a straight line that best represents the data on a scatter plot.   This line may pass through some of the points, none of the points, or all of the points. Example.

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Modeling Relationships with a Line

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Modeling relationships with a line

Modeling Relationships with a Line

Math Notebook


Line of best fit

Line of Best Fit

A line of best fit  (or "trend" line) is a straight line that best represents the data on a scatter plot.  

This line may pass through some of the points, none of the points, or all of the points.


Example

Example

Is there a relationship between the fat grams and the total caloriesin fast food?


Correlations

Correlations

Positive Correlation: y tends to increase as x increases

Negative Correlation: y tends to decrease as x increase

Relative to no correlation: no apparent correlation


In your notebooks

In your Notebooks

Can we predict the number of total calories based upon the total fat grams?

Step 1: Create a Scatter plot


Straight edge

Straight Edge

 Step 2: Using a straight edge, position the straight edge so that the plotted points are as close to the strand as possible.

Step 3: Then, find two points that you think will be on the "best-fit" line. 


I picked

I picked

I picked the the points (9, 260) and (30, 530).  You may choose different points. 

.Step 4: Calculate the slope of the line through your two points (rounded to three decimal places; thousandths place)


Slope formula

Slope Formula

Does anyone remember our slope formula?

Step 5: Write the equation of the line


Predicting

Predicting

This equation can now be used to predict information that was not plotted in the scatter plot.  

Predicting:- If you are looking for values that fall within the plotted values, you are interpolating.- If you are looking for values that fall outside the plotted values, you are extrapolating.

Be careful when extrapolating.  The further away from the plotted values you go, the less reliable is your prediction.


Remember

Remember

We chose two points to form our line-of-best-fit. 

It is possible, however, that someone else will choose a different set of points, and their equation will be slightly different.  Your answer will be considered CORRECT, as long as your calculations are correct for the two points that you chose. 

So, if each answer may be slightly different, which answer is the REAL "line-of-best-fit?


Investigation

Investigation

Kendra likes to watch crime scene investigation shows on television. She watched a show where investigators used a shoe print to help identify a suspect in a case.

She questioned how possible it is to predict someone’s height is from his shoe print.

To investigate, she collected data on shoe length (in inches) and height (in inches) from 10 adult men.


Modeling relationships with a line

Create a scatter plot of this data


Relationship

Relationship?

Is there a relationship between shoe length and height?

How would you describe the relationship? Do the men with longer shoe lengths tend be taller?


Models to make predictions

Models to Make Predictions

When two variables “x” and “y” are linearly related, you can use a line to describe their relationship.

You can also use the equation of the line to predict the value of the y-variable based on the value of the x-variable.


Example1

Example

The equation of a line y = 25.3 +3.66x might be used to describe the relationship between shoe length and height,

Where x represents shoe length and y represents height.

To predict the height of a man with a shoe length of 12, you would substitute 12 in for “x” in the equation of the line and then calculate the value of “y”


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