5. Calculating the Pearson correlation and the coefficient of determination
Suppose you are interested in seeing whether the total number of days students are absent from high school correlates with their grades. You obtain school records that list the total absences and average grades (on a percentage scale) for 80 graduating seniors.
You decide to use the computational formula to calculate the Pearson correlation between the total number of absences and average grades. To do so, you call the total number of absences \(\mathrm{X}\) and the average grades \(Y\). Then, you add up your data values \((\Sigma X\) and \(\Sigma Y)\), add up the squares of your data values \(\left(\Sigma X^{2}\right.\) and \(\left.\Sigma Y^{2}\right)\), and add up the products of your data values ( \(2 \mathrm{XY}\) ). The following table summarizes your results:
Sigma X | 380 |
---|---|
Sigma Y | 5,820 |
SigmaX^(2) | 2,708 |
Sigma Y2 | 440,838 |
Sigma xy | 26,709 |
The sum of squares for average grades is \(\mathrm{SS}_{y}=\)
The sum of products for the total number of absences and average grades is \(\mathrm{SP}=\)
The Pearson correlation coefficient is \(r=\)
Suppose you want to predict average grades from the total number of absences among students. The coefficient of determination is \(r^{2}=\) , indicating that of the variability in the average grades can be explained by the relationship between the average grades and the total number of absences.
When doing your analysis, suppose that, in addition to having data for the total number of absences for these students, you have data for the total number of days students attended school. You'd expect the correlation between the total number of days students attended school and the total number of absences to be correlation between the total number of days students attended school and average grades to be
5. Calculating the Pearson correlation and the coefficient of determination
For the data below, compute the Pearson correlation. 4 6. Find coefficient of determination: 5. 2. 3. 2.
Q7. What is the coefficient of determination? Q11. State which correlation coefficient (Pearson, Spearman, point-biserial, or phi) should be used given the following information. Both factors are interval or ratio scale. Both factors are ranked. One factor is dichotomous, and the other factor is continuous. Both factors are dichotomous. Q13. State whether each of the following is an example of a positive correlation or a negative correlation. Higher education level is associated with a larger annual income. Increased testosterone is...
4. Scatter plots and calculating correlation Suppose you are given the following five pairs of scores: XY61926384110Create a scatter plot of these scores in the following diagram. For each of the five (X,Y) pairs, click on the plotting symbol (the black X) in the upper right corner of the tool, and drag it to the appropriate location on the grid. Based on your scatter plot, you would expect the correlation to be _______ .The mean X score is Mx = _______ , and...
Compute the Pearson Correlation Coefficient, r, for the following data X Y 1 7 3 4 5 3 4 2 2 4 Note: If it is a decimal number with two or more than two places, leave only two decimal places after the decimal point and do not round. If it is a negative correlation, please do not forget to include the negative sign. 1a) The Pearson Correlation, r is: 1b) The correlation is Group of answer choices a) Medium...
Determine the Pearson product-moment correlation coefficient for the following data. x 1 10 9 6 4 3 2 y 9 4 4 5 7 7 10 (Do not round the intermediate values. Round your answer to 3 decimal places.) Correlation coefficient, r
A. Find the linear correlation coefficient. B. Find the least-squares regression line. C.Using the model above, predict grade for 22 absences. Note: Please, if you use any values from the tables, indicate which table they come from. Also, please write clearly on a piece of paper. The data set below is on student absences and final grade. Sludem untudcat Student | Number of absences x | Final grade y (%) 82 86 43 74 58 90 78 15 12 Assume...
2a. Based on the above sample, is the population Pearson correlation coefficient significantly different from 0 at the 0.01 level? 2b. Is the population Pearson correlation coefficient significantly smaller than 0 at the 0.01 level? 3.5 la. The table gives the weight (x) (in 1000 lbs.) and highway fuel efficiency () (in miles/gallon) for a sample of 13 cars. Use the table to assist your calculations Vehicle X Y X-Mx Y-My (X-Mx)(Y-My) (X-Mx) (Y-My)? Chevrolet Camaro 30 Dodge Neon 2.6...
Assuming everything else stays the same, does the value of the Pearson correlation coefficient change if the mean for the X values is now 600 and the mean for the Y values is 400? Why or why not?
1. Which is not true of R², the coefficient of determination ? a It is the square of the coefficient of correlation. b. It is calculated using sums of squares (e.g., SSR, SSE, SST). c. It reports the percent of the variation in Y explained by X. d. It is negative when there is an inverse relationship between X and Y.
This question asks you to compute the sample correlation coefficient (?xy ) and estimate the regression coefficients with ordinary least squares (OLS) “by hand” for the model (Yi = ?1 + ?2Xi +ui) using the data below, but without using R (except to get critical values or p‐values, and to check your work) y x 1 2 5 6 4 4 4 6 1 2 A. Compute and report the sample correlation coefficient B. Can you reject the null hypothesis...