![]() As we rotate our line further and further clockwise we once again pass the perfectly horizontal line (r=0), but this time we are moving into positive territory i.e. A line which is a 'perfect opposite' of r=1 will be r=-1 i.e a downwards sloping line.īut this cannot go on forever. ![]() As this line moves further and further from the line which has an r of 0 we are getting closer to the 'opposite' of the line which had an r of positive 1. Do you see what I am getting at? Now r has a negative value. Let's continue rotating our imaginary line clockwise.now we are moving 'beneath' the line which has an r of 0 so we are moving into negative territory. (Which btw means that a change in X results in no change in Y). Now let's rotate our line clockwise.until the line is a straight horizontal line. This line (r=1) is an upwards sloping line. Here, when we say that r has a value of 1 we are basically saying that on average an increase in X will result in an increase in Y. When it comes to telling the time we refer to the angle of the minute hand by splitting the clock into 60. So imagine the minute hand on a clock which can rotate 360 degrees but is pinned down to the centre of the clock. The least squares line will always go through the mean of X and the mean of Y. ![]() In this example, 71.99% of the variation in the exam scores can be explained by the number of hours studied.8:09 ). It is the proportion of the variance in the response variable that can be explained by the explanatory variable. This value is known as the coefficient of determination. We can also see that the r-squared for the regression model is r 2 = 0.7199. We can use this estimated regression equation to calculate the expected exam score for a student, based on the number of hours they study.įor example, a student who studies for three hours is expected to receive an exam score of 85.25:Įxam score = 68.7127 + 5.5138*(3) = 85.25 We interpret the coefficient for the intercept to mean that the expected exam score for a student who studies zero hours is 68.7127. We interpret the coefficient for hours to mean that for each additional hour studied, the exam score is expected to increase by 5.5138, on average. The following output will automatically appear:įrom the results, we can see that the estimated regression equation is as follows: Scroll down to Calculate and press Enter. Press Stat and then scroll over to CALC. Then scroll down to 8: Linreg(a+bx) and press Enter.įor Xlist and Ylist, make sure L1 and L2 are selected since these are the columns we used to input our data. Enter the following values for the explanatory variable (hours studied) in column L1 and the values for the response variable (exam score) in column L2: ![]() To explore this relationship, we can perform the following steps on a TI-84 calculator to conduct a simple linear regression using hours studied as an explanatory variable and exam score as a response variable.įirst, we will input the data values for both the explanatory and the response variable. Press Stat and then press EDIT . Suppose we are interested in understanding the relationship between the number of hours a student studies for an exam and the exam score they receive. ![]() Example: Linear Regression on a TI-84 Calculator This tutorial explains how to perform linear regression on a TI-84 calculator. Linear regression is a method we can use to understand the relationship between an explanatory variable, x, and a response variable, y. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |