Question

Using a calculator to determine the line of best fit for these data, where x is the number of years since 1980. Round all coefficients to 4 decimal places.

What is the correlation, r? What does it mean about whether this line is a good fit for these data? Explain.

Give the slope of the line and explain what it means.

Use this equation to predict the number of women in the House of Representatives in the year 2013.

I am starting a new unit in math and don't understand what to put in calculator. Any help is greatly appreciated. Below I will try my best to add the table. Commas separate each column.

Year, x, Women in House
1980, 0, 19
1984, 4, 22
1988, 8, 25
1992, 12, 47
1996, 16, 51
2000, 20, 59
2004, 24, 68
2008, 28, 78

Answer 1

calculator instructions will depend on the model/type you have.
- scientific calculator (TI-36pro)
may be a "data" button that opens a table where you can input values.
put the x-values (0,4,8,...) into the first column and the y-values (19,22,25,...) into the second column.
after inputting the values back out and find a "stat-reg/distr" button. Then find the linear regression option "LinReg" or "ax+b"
these setting should already be set but just in case:
x = first column
y = second column
hit calculate
calculator gives the coefficients for the linear equation : y = 2.2292x + 14.9170
r^2 = 0.9682

the r^2 value tells you how well the equation fits the data or how good it will be a predicting unknown values. The closer r^2 is to 1 the better fit it is.

the slope of the line is 2.2292. I'm guessing from the next question.. he data represents women in the house of representatives. If this is the case then the slope represents how many more women per year are in the house of representatives.

2013 - 1980 = 33
This is the x-value you use to find the number of women in the house of representatives in 2013 since x=0 is 1980.
plug this into the equation and solve for y.
y = 88.4806

* you can also use Microsoft excel to generate this information fairly easily instead of a calculator. Just enter the data into columns, highlight them, go to insert tab, click the scatter plot chart (bunch of dots) then right click the dots on the graph and add trendline. check display equation and r^2 value