The marks obtained by 10 students in statistics (x) and algebra (y) are as follows:Table 688827367625756545348y71536756515062465242a. Calculate the coefficient of correlation using:i.Pearson's formula and comment on your answer.ii.Spearman's rank and comment on your answer.b. Find the least squares regression equation and calculate the expectedvalue ofyifX = 50.c. Construct a scatterplot and comment on the linear relationship betweenx and y.

Correlation Coefficient: Let (x1, y1), (x2, y2), ... , (xn, yn) be n set of observations for the…

Answered: The marks obtained by 10 students in…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The data below are the final exam scores of 10 randomly selected statistics students and the number of hours they studied for the exam. Calculate the correlation coefficient r. Hours, x 8 10 7 13 7 9 9 10 11 8 Scores, y 72 87 67 95 73 85 92 97 97 78 Question content area bottom Part 1 A. 0.991 B. 0.847 C. 0.761 D. 0.654
A biologist looked at the relationship between number of seeds a plant produces and the percent of those seeds that sprout. The results of the survey are shown below. Seeds Produced 65 51 59 66 42 62 61 69 65 Sprout Percent 64.5 65.5 64.5 49 72 61 50.5 54.5 50.5 Find the correlation coefficient: r=r= Round to 3 decimal places. The null and alternative hypotheses for correlation are:H0:H0: == 0H1:H1: ≠≠ 0 The p-value is: ? (Round to 5 decimal places) r2 = ? (Round to 3 decimal places)
Research was conducted on the amount of training for 5K race and the time a contestant took to run the race. The researcher recorded the number of miles a contestant ran during the last month of training and the time it took the contestant to complete the 5K. The results are below. Miles Trained 65 78 90 91 104 112 Time (Minutes) 23 26 34 39 42 50 (a) Give the correlation coefficient. Round to one decimal place. (b) Use technology to write the regression equation that predicts the time it takes a contestant to complete the race by using the miles trained as the explanatory variable. Complete the missing parts of the equation below, rounding values to one decimal place. ý (c) Interpret the y-intercept in the context of this scenario. O Each additional mile of training reduces the time needed to complete the 5K by 0.6 minutes. A contestant who has not trained at all in the last month can expect to complete the 5K in 0.6 minutes. X O A contestant who has not trained at all in the last…
Here is a bivariate data set. x y 74 43 80 45 89 12 72 43 75 37 82 31 79 60 57 68 71 34 Find the correlation coefficient and report it accurate to four decimal places.r =
A biologist looked at the relationship between number of seeds a plant produces and the percent of those seeds that sprout. The results of the survey are shown below. Seeds Produced 44 69 42 45 57 51 59 43 40 Sprout Percent 61 50.5 72 71.5 54.5 60.5 56.5 63.5 62 Find the correlation coefficient: r=r= Round to 3 decimal places. The null and alternative hypotheses for correlation are:H0:H0: == 0H1:H1: ≠≠ 0 The p-value is: ? (Round to 5 decimal places)
The data below show the Marks scored by eight IT students in two tests: Probability and Statistics(X) ,and Programming (Y). X 67 42 85 51 39 97 81 70 Y 70 59 71 38 55 62 80 75 Calculate product moment correlation coefficient
Run a regression analysis on the following bivariate set of data with y as the response variable. x y 61.1 78.9 58.6 84.5 70.2 58.1 62.3 65.4 64.2 68.9 58 84.1 63.7 70.2 64.6 71.9 68.3 71.5 61.7 77.5 59.3 77.4 64.6 71.2 Find the correlation coefficient and report it accurate to three decimal places.r = What proportion of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place. (If the answer is 0.84471, then it would be 84.5%...you would enter 84.5 without the percent symbol.)r² = %Based on the data, calculate the regression line (each value to three decimal places)y = x + Predict what value (on average) for the response variable will be obtained from a value of 61.9 as the explanatory variable. Use a significance level of α=0.05α=0.05 to assess the strength of the linear correlation.What is the predicted response value? (Report answer accurate to one decimal place.)
The data below are the final exam scores of 10 randomly selected statistics students and the number of hours they studied for the exam. Calculate the correlation coefficient r. Hours, x 1 3 0 6 0 2 2 3 4 1 Scores, y 67 82 62 90 68 80 87 92 92 73 Question content area bottom Part 1 A. 0.991 B. 0.847 C. 0.761 D. 0.654
A biologist looked at the relationship between number of seeds a plant produces and the percent of those seeds that sprout. The results of the survey are shown below. Seeds Produced 48 48 42 51 56 43 53 Sprout Percent 59 68 60 55.5 49 64.5 48.5 a. Find the correlation coefficient: r = Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho: pv H1: pv = 0 The p-value is: (Round to four decimal places) c. Use a level of significance of a = 0.05 to state the conclusion of the hypothesis test in the context of the study. O There is statistically significant evidence to conclude that a plant that produces more seeds will have seeds with a lower sprout rate than a plant that produces fewer seeds. O There is statistically insignificant evidence to conclude that there is a correlation between the number of seeds that a plant produces and the percent of the seeds that sprout. Thus, the use of the regression line is not appropriate. O There is statistically…
The table below gives the estimated world population (in billions) for various years. 1980 1990 1997 2000 2005 2011 Years Population 4400 5100 5852 6080 6450 7000 What is the value of the correlation coefficient (r)? O 0.558 Ⓒ -0.894 0.998 O- 0.489

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