Math Notebook

 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.

 Is there a relationship between the fat grams and the total calories in fast food? Total Fat (g) Total Calories Hamburger9260 Cheeseburger13320 Quarter-Pounder21420 Big Mac30560 Grilled Chicken20440 Grilled Chx w/ Chz25510 Fish Fillet28560 Crispy Chicken25500 Chicken Nuggets30600 Quarter Pounder w/ Chz Arch Special w/ Bacon 34590

 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

 Can we predict the number of total calories based upon the total fat grams?  Step 1: Create a Scatter plot

 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 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)

 Does anyone remember our slope formula?  Step 5: Write the equation of the line

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

 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?

 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.

x = Shoe LengthY = Height inches inches inches inches inches inches inches inches inches inches Create a scatter plot of this data

 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?

 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.

 The equation of a line y = x 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”