MATH 225N Week 8 Final Exam Study Guide

Math 225 final exam study guide 1.) Below are the three types of scatter plots that can occur in a graph. 144780042856 Positive linear pattern with deviations, we can see that as the x-values decrease, the y- values increase. So it is a positive relationship. But there are points that deviate from the positive linear pattern, so it is a weaker pattern, instead of a strong one. 1447800223856 Negative linear pattern with deviations, we can see that as the x-values increase, the y- values decrease. So it is a negative relationship. But there are points that deviate from the negative linear pattern, so it is a weaker pattern, instead of a strong one. 143827547672 No pattern, we see that the points are all over, so no pattern can be determined. 14438622245352.) 3.) Suppose you computed r = −0.745 using n = 25 data points. Using the critical values table below, determine if the value of r is significant or not. df CV (+ and -) df CV (+ and -) df CV (+ and -) df CV (+ and -) 91469225180810.997110.555210.413400.304 20.950120.532220.404500.273 91469225247430.878130.514230.396600.250 40.811140.497240.388700.232 91469225248750.754150.482250.381800.217 60.707160.468260.374900.205 70.666170.456270.3671000.195 91469225248780.632180.444280.361 90.602190.433290.355 100.576200.423300.349 91469252418 EXPLANATION There are n−2 = 25−2 = 23 degrees of freedom. Looking at the table of critical values, the critical values corresponding to df = 23 are −0.396 and 0.396. Since the value of r is less than −0.396, r is significant. So we could say, r is significant because it is not between the positive and negative critical values. If r equaled a value between these critical values then we would say r is not significant because it is between the positive and negative critical values. Brandon is studying the relationship between the time spent sewing a blanket per day and the length put on the blanket in millimeters per day and has collected the data shown in the table. The line of best fit for the data is y = 0.342x – 42.05. Assume the line of best fit is significant and there is a strong linear relationship between the variables. X=time spent sewing blanket Y=time till blanket is finished 150 10 180 19 200 25 225 36 According to the line of best fit, what would be the predicted length of the millimeters for someone who spent 175 minutes sewing? Round your answer to two decimal places, as needed. Explanation Substitute 175 for x into the line of best fit to estimate the length in millimeters for someone who spent 175 minutes sewing: y = 0.342(175) – 42.05 = 17.8 millimeters. A scientific experiment on skingrowth gives the following data table. x y 78 49 84 63 92 85 84 108 93 122 The least squares regression line was found. Using technology, it was determined that the total sum of squares (SST) was 5968.8 and the sum of squares of regression (SSR) was 5593.7 . Calculate R2, rounded to three decimal places. EXPLANATION 3940175204349𝑅2 = 𝑆𝑆𝑅 896416109970𝑆𝑆𝑇 3844163339630𝑅2 = 5593.7 8964161084725968.8 𝑅2 = 0.937 The data