Question

example 2
in a study of the factors that affect success in a calculus course, data were collected for 10 different people. scores on an algebra placement test are given along with their calculus achievement scores. can scores on algebra tests be used to predict success in calculus classes? to answer this question, look at a scatterplot on your calculator.
algebra: 17 21 11 16 15 11 24 27 19 8
calculus: 73 66 64 61 70 71 90 68 84 52
a.) use the calculator to create a scatterplot and calculate the correlation coefficient.
b.) describe the strength, form and direction of the scatterplot.
regression
least squares regression line model: \\(\hat{y}=mx + b\\)
calculator procedures
least squares regression lines on the ti - 84 plus
step 1: enter the x - values into l1 and the y - values into l2.
step 2: press stat and the right arrow key to access the calc menu.
step 3: select the linreg(ax + b) and run the command.
given a point (x,y) on a scatterplot, and the least - squares regression line \\(\hat{y}=mx + b\\), the for the point (x,y) is the difference between the observed value y and the predicted value \\(\hat{y}\\).

Explanation:

Step1: Enter data into calculator

Enter algebra scores as \(x -\)values into list L1 and calculus scores as \(y -\)values into list L2 on the TI - 84 Plus calculator.

Step2: Access statistics menu

Press STAT and then the right - arrow key to access the CALC menu.

Step3: Select linear regression

Select LinReg\((ax + b)\) from the CALC menu and run the command. This will give the correlation coefficient \(r\).

Step4: Analyze scatter - plot

To describe the strength, form and direction of the scatter - plot:

• Strength: If \(|r|\) is close to 1, it is a strong correlation. If \(|r|\) is close to 0, it is a weak correlation.
• Form: Check if the points seem to follow a linear (straight - line) or non - linear pattern.
• Direction: If \(r>0\), it is a positive correlation (as \(x\) increases, \(y\) increases). If \(r < 0\), it is a negative correlation (as \(x\) increases, \(y\) decreases).

Answer:

a. Use the TI - 84 Plus calculator steps as described above to create scatter - plot and calculate the correlation coefficient \(r\).
b. The strength is determined by the magnitude of \(r\), the form is checked for linearity, and the direction is determined by the sign of \(r\).