In the following problems, find the equation of the least squared regression line and the correlation coefficient. Then perform a hypothesis test to determine if there is a significant relationship between the two variables. Use the p-value method and show all 5 steps of the hypothesis test. Test at a= 0.05 . 1. The numbers of faculty and students are shown for a random selection of small colleges. Faculty, x 99 110 113 116 138 174 220 Students, y 1353 1290 1091 1213 1384 1283 2075

In the following problems, find the equation of the least squared regression line and the correlation coefficient. Then perform a hypothesis test to determine if there is a significant relationship between the two variables. Use the p-value method and show all 5 steps of the hypothesis test. Test at a= 0.05 . 1. The numbers of faculty and students are shown for a random selection of small colleges. Faculty, x 99 110 113 116 138 174 220 Students, y 1353 1290 1091 1213 1384 1283 2075

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Q1 Collect sufficient data about any two quantitative variables (logically correlated) using reasonable sets of values (At least 20 values). Use Microsoft Excel and answer the following: First: Determine the independent variable and the dependent variable. Second: Make the correlation analysis, determine the correlation coefficient, and interpret it. Third: Conduct the regression analysis and answer the following questions: What is the type of regression in your example? Write the sample size. Find the degrees of freedom. Find the value of the coefficient of determination, and interpret it. Is your model valid? Why? Is the independent variable having a significant effect on the dependent variable? Why? Write down the regression line equation. Estimate the value of ŷ at any value of X.
Consider a panel data set and the following regression model. Yit Bo + B₁Xit + ++ Uit What do subscripts / and t refer to? O A. Subscripts i and tidentify different time periods. O B. Subscripts / and t identify the entity and time period respectively. OC. Subscripts i and t identify different individuals. O D. Subscripts i and t identify the time period and entity respectively.
ANSWER D ONLY
R3
9. Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (Each pair of variables has a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The caloric content and the sodium content (in milligrams) for 6 beef hot dogs are shown in the table below. Calories, x Sodium, y 160 130 330 120 70 190 (a) x = 170 calories (c) x = 150 calories 180 (b) x = 80 calories 420 470 360 250 530 (d) x = 210 calories Find the regression equation. x+( (Round to three decimal places as needed.) y = Choose the correct graph below. OA. О В. OC. OD. 560- 560 560 560- 200 G 0IN T> 200 200 Calories Calories Calories Calories (a) Predict the value of y for x = 170. Choose the correct answer below. O A. 411.632 O B. 543.752 O C. 455.672 O D. not meaningful (b) Predict the value of y for x = 80. Choose the correct answer below. O A. 411.632 О В. 257.492 O C.…
In the following problems, find the equation of the least squared regression line and the correlation coefficient. Then perform a hypothesis test to determine if there is a significant relationship between the two variables. Use the p-value method and show all 5 steps of the hypothesis test. Test at a= 0.05 2. A random sample of scoring leaders in the NHL showed the following numbers of assists and total points. Assists, x 26 29 32 34 36 37 40 Total Points, y 48 68 66 69 76 67 84
Suppose you are a dolphin trainer at SeaWorld. You teach the dolphins by rewarding them with fish treats after each successful attempt at a new trick. The following table lists the dolphins, the number of treats per success given to each, and the average number of attempts necessary for each to learn to perform the tricks. Dolphin Number of Treats Number of Attempts Diana 2 Frederick 4 Fatima Marlin Ŷ = bX + a You can use the preceding sample data to obtain the regression line, where Ŷ is the predicted value of Y: b = One formula for the slope of the regression line is as follows: SP = To calculate the slope, first calculate SP and SSx: 1 3 and SSx = ∞587 (Hint: For SP use the computational formula and for SSx use the definitional formula.) The slope of the regression line is Frederick Fatima Marlin The difference between Y and Ŷ for a particular sample point (observation) is called a residual. Calculate the predicted Y (Y) for each of the dolphins, and then calculate the residuals. 4…
Post secondary education information was examined for a random selection of states. The data below show the number of community colleges in the number of universities for each particular state. Community: 12, 17, 13, 10, 8 University: 4, 6, 5, 4, 3 A. Create a scatterplot of the given data sets B. Find the correlation coefficient of the sets of data. C. Create the equation of the regression line for the data and evaluate it when X=300.
The coefficient of determination (r2) is a measure of the: a.) amount of variance in the dependent variable explained by the independent variable. b.) correlation between two variables. c.) variability of the dependent measure. d.) slope of a regression line.
Suppose you are a dolphin trainer at SeaWorld. You teach the dolphins by rewarding them with fish treats after each successful attempt at a new trick. The following table lists the dolphins, the number of treats per success given to each, and the average number of attempts necessary for each to learn to perform the tricks. Dolphin Number of Treats Number of Attempts Diana 4 5 Frederick 2 8 Fatima 1 8 Marlin 3 7 You can use the preceding sample data to obtain the regression line, where Ŷ is the predicted value of Y: ŶŶ = = bX + abX + a One formula for the slope of the regression line is as follows: bb = = SPSSxSPSSx To calculate the slope, first calculate SP and SSxx: SP = __?__ , and SSxx = _?_ . (Hint: For SP use the computational formula and for SSxx use the definitional formula.) The slope of the regression line is , and the Y intercept of the regression line is ___?__ . The difference between Y and…
Write your complete solutions. The final test and exam averages for 20 randomly selected students taking a course in engineering statistics and a course in operations research are in the table below. Assume that the final averages are jointly normally distributed. (a) Find the regression line relating the statistics final average to the OR final average. Graph the data. (b) Test for significance of regression using a = 0.05. (c) Estimate the correlation coefficient. (d) Test the hypothesis that p = 0, using a = 0.05. (e) Test the hypothesis that p = 0.5, using a = 0.05. equations on this slide to answer the question) (f) Construct a 95% confidence interval for the correlation coefficient. Statistics OR Statistics OR Statistics OR 86 80 86 81 83 81 75 81 71 76 75 69 75 65 72 71 75 81 84 85 90 92 71 72 94 95 62 65 83 80 90 93 76 84 97 70 73 72 80 98