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**Unformatted text preview: **Scatter Plots, Correlation, and Regression One way to see whether two variables are related is to graph them. For instance, a researcher wishes to determine whether there is a relationship between grades and height. A scatter plot will help us see whether the two variables are related. If you check the handouts, you will see how to use Excel to do a scatter plot. Scatter Plot: Example 1 Example: Y (Grade) 100 95 90 80 70 65 60 40 30 20 X (Height) 73 79 62 69 74 77 81 63 68 74 Height is in inches (r = .12; r 2 = .01; we will learn about r and r-squared later. An r, correlation coefficient of .12 is very weak. In this case we will find out that it is not significant, i.e., we have no evidence to reject the null hypothesis that the population correlation coefficient is 0.) Note that the two variables do not appear to be related. Later, we will learn how to use the correlation coefficient will give us a measure to determine how weakly or strongly two variables are related. Scatter Plot: Example two this ones a little better. From the scatter plot below, we see that there appears to be a positive linear relationship between hours studied and grades. In other words, the more one studies the higher the grade (I am sure that this is a big surprise). Y (Grade) 100 95 90 80 70 65 60 40 30 20 X (Hours Studied) 10 8 9 8 7 6 7 4 2 1 (r = .97 We did not learn this yet but a correlation coefficient of .97 is very strong. The coefficient of determination, r 2 = .94 We will learn about this later. = 8.92 + 9.05X ; This is the regression equation and we will also learn about this later.) Scatter Plot Example 3 X (price) Quantity Demanded $2 95 3 90 4 84 5 80 6 74 7 69 8 62 9 60 10 63 11 50 12 44 This is an example of an inverse relationship (negative correlation). This is an example of an inverse relationship (negative correlation)....

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