Question

The following table shows the test scores and sleep averages of several students. Hours of sleep (x) 7 7 7 6 8 8 9 5 6 7 7 9 8 8 10 8 Test score (y) 90 75 70 70 85 95 90 60 65 80 70 85 85 100 95 90 (a) Use graphing technology (TI calculator or Desmos) to find the linear regression equation that models the data. Let x equal the hours of sleep and y equal test score. Explain the steps you use.

Answer 1

To find the linear regression equation that models the data, use graphing technology such as a TI calculator to enter the sleep and test score data into lists, calculate the linear regression, and obtain an equation of the form y = ax + b, representing the relationship.

Step-by-step explanation:

To find the linear regression equation that models the relationship between hours of sleep (x) and test scores (y), you can use graphing technology like a TI calculator or Desmos. Here’s a step-by-step explanation of how to do this using a TI calculator:

1. Enter the data into two lists. Press the STAT button, then choose EDIT. Enter the hours of sleep data into L1 and the test scores data into L2.
2. After entering the data, press the STAT button again. Move to the CALC menu using the arrow keys and choose option 4: LinReg(ax+b).
3. Press the 2ND button, then the number corresponding to L1 to choose the L1 list, press the comma button, and do the same for the L2 list.
4. Press ENTER to calculate the linear regression equation. You will be given an equation in the form y = ax + b, where 'a' is the slope, and 'b' is the y-intercept.

This regression equation can be used to predict the test score given a certain amount of sleep hours.