Mentor: A line of best fit is often useful to attempt to represent data with the equation of a straight line in order to predict values that may not be displayed on the plot. The line of best fit is determined by the correlation between the two variables on a scatter plot.
Q. Is it reasonable to use this line of best fit to make the above prediction?
Correct answer: The estimate, a predicted time of 46.92 minutes, is both reliable and reasonable. The data in the table only includes studying times between 50 and 110 minutes, so the line of best fit gives reliable and reasonable predictions for values of x between 50 and 110 .
Table of Contents
- Q. Is it reasonable to use this line of best fit to make the above prediction?
- Q. How do you predict a scatter plot?
- Q. What is the most common criterion used to determine the best fitting line?
- Q. How do you find predictions in statistics?
- Q. How do you predict a regression line?
- Q. How many regression lines are there?
- Q. What does a positive regression line mean?
- Q. When would you use a regression line?
Q. How do you predict a scatter plot?
- Scatter Plots show a positive trend if y tends to increase as x increases or if y tends to decrease as the x decreases.
- Scatter Plots show a negative trend if one value tends to increase and the other tends to decrease.
- A scatter plot shows no trend (correlation) if there is no obvious pattern.
Q. What is the most common criterion used to determine the best fitting line?
The most common criterion used to determine the best-fitting line is the line that minimizes the sum of squared errors of prediction. This line does not need to go through any of the actual data points, and it can have a different number of points above it and below it.
Q. How do you find predictions in statistics?
Statistical researchers often use a linear relationship to predict the (average) numerical value of Y for a given value of X using a straight line (called the regression line). If you know the slope and the y-intercept of that regression line, then you can plug in a value for X and predict the average value for Y.
Q. How do you predict a regression line?
We can use the regression line to predict values of Y given values of X. For any given value of X, we go straight up to the line, and then move horizontally to the left to find the value of Y. The predicted value of Y is called the predicted value of Y, and is denoted Y’.
Q. How many regression lines are there?
There are two lines of regression.
Q. What does a positive regression line mean?
The sign of a regression coefficient tells you whether there is a positive or negative correlation between each independent variable and the dependent variable. A positive coefficient indicates that as the value of the independent variable increases, the mean of the dependent variable also tends to increase.
Q. When would you use a regression line?
A regression equation is used in stats to find out what relationship, if any, exists between sets of data. For example, if you measure a child’s height every year you might find that they grow about 3 inches a year. It’s not very common to have all the data points actually fall on the regression line.
