Linear Regression
SECONDARY 1 MATH
Linear Regression
a mathematical technique for finding the straight line that best
fits the values of a scatter plot of two-variable data points
if a best fit line is found, it can be used as the basis for estimating
future values of the data by extending it and maintaining the slope
World’s Tallest Man – Robert Pershing Wadlow (1918-1940)
The tallest man in medical history for whom there is irrefutable evidence is Robert Pershing Wadlow. He was born at Alton, Illinois, USA, on February 22, 1918, and when he was last measured on June 27, 1940, was found to be 2.72 m (8 ft 11.1 in) tall. His great size and his continued growth in adulthood were due to hypertrophy of his pituitary gland which results in an abnormally high level of human growth hormone. He showed no indication of an end to his growth even at the time of his death.��Wadlow died at 1:30 a.m. on July 15, 1940, in a hotel in Manistee, Michigan, as a result of a septic blister on his right ankle caused by a brace, which had been poorly fitted only a week earlier. He was buried in Oakwood Cemetery, Alton, in a coffin measuring 3.28 m (10 ft 9 in) long, 81 cm (32 in) wide and 76 cm (30 in) deep.
Robert next
to his father
Make a scatter plot of the
data on a graphing calculator
In List1, type the values from the “Age” column
In List2, type the values from the “Height” column
STAT PLOT 🡪 “ON” and select the Scatter Plot Icon
Specify the Xlist: L1
Ylist: L2
Mark: ☐
Adjust the Window to show the data
Xmin: 0 Xmax: 25
Ymin: 0 Ymax: 150
Age (years)
Height (inches)
Calculate the linear
regression line
STAT 🡪 CALC
“LinReg(ax+b)”
Specify Xlist: L1
Ylist: L2
FreqList: leave blank
What is the slope? What does the slope tell you about the situation?
a = 2.57
Robert Pershing Wadlow was growing
about 2.57 inches every year
What is the y-intercept? What does the y-intercept tell you about
the situation?
b = 51.85
At birth, the equation suggests that Robert Pershing
Wadlow would have been 51.85 inches tall
Note: This is NOT likely to have a baby born with that length.
The equation has limitations
Use the linear regression line to estimate how tall Robert would
have been at age 25? At 40 years?
25 years old 40 years old
Use the linear regression line to estimate how old Robert would
have been when he reached a height of 15 feet tall?
15 feet = 180 inches
If Robert had lived 49.86 years
and kept the same growth rate
he could have been 15 feet tall
116.1 inches tall
(9’ 8”)
154.65 inches tall
(12’ 11”)
x = 49.86
Each year the US Census Bureau provides income statistics for the United States. In the years from 1991 to 2005, they provided the data in the table.
(All dollar amounts have been adjusted for the rate of inflation so that they are comparable from year-to-year.)
Let x be the years since 1990
Let y be the Median Income
for All Women
Make a scatter plot of the
data on a graphing calculator
Adjust the Window to see
all of the data
Note: if you enter the actual year into List 1 (1991, 1992, etc.) your regression equation gives a y-intercept 2000 years ago…
This is not useful since U.S.A. wasn’t a country yet and women’s income not measurable at that time
Year since 1990
Calculate the linear
regression equation
Median Income ($)
What is the slope? What does the slope tell you about the situation?
a = 464.10
Since 1990 the median income for women has risen
about $464.10 every year
What is the y-intercept? What does the y-intercept tell you about
the situation?
b = 18052.60
We predict that in 1990 the median income for women
would have been $18052.60.
Use the linear regression line to estimate the Median income for
women in the United States in 2015
2015 is 25 years since 1990
Use the linear regression line to estimate the year that the average
income for women in the United States will be $50000.
We predict that the median
income for women in the U.S.
will be $50000 in the year 2059
In 2015 we predict that the median income for
women in the U.S. is $29655.10
x = 68.84