a) Find the least square regression line for the following set of data {(-1 , 0),(0 , 2),(1 , 4),(2 , 5)} b) Plot the given points and the regression line in the same rectangular system of axes.
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a) Find the least square regression line for the following set of data
{(-1 , 0),(0 , 2),(1 , 4),(2 , 5)}
b) Plot the given points and the regression line in the same rectangular system of axes.
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- Does Table 1 represent a linear function? If so, finda linear equation that models the data.Consider the set of points (0,9),(1,5),(6,3) and (9,2). In this set of points, the age of a dolphin is the first part of each ordered pair and the second part is the number of tricks that the dolphin learned in a month. So, the 6 year-old dolphin learned 3 tricks in the month. Write the least squares regression line for this data. Use the line to estimate how many tricks a 4 year-old dolphin could learn. Then find r and r2. Explain what r2 means.The applet displays a scatterplot with the following points: (7,10),(27,35),(24,25),(8,12),(10,19),(15,22). Identify the slope of the regression line, intercept of the regression line, and correlation coefficient. Report your answers accurate to within two decimal places.
- We have data on Lung Capacity of persons and we wish to build a multiple linear regression model that predicts Lung Capacity based on the predictors Age and Smoking Status. Age is a numeric variable whereas Smoke is a categorical variable (0 if non-smoker, 1 if smoker). Here is the partial result from STATISTICA. b* Std.Err. of b* Std.Err. N=725 of b Intercept Age Smoke 0.835543 -0.075120 1.085725 0.555396 0.182989 0.014378 0.021631 0.021631 -0.648588 0.186761 Which of the following statements is absolutely false? A. The expected lung capacity of a smoker is expected to be 0.648588 lower than that of a non-smoker. B. The predictor variables Age and Smoker both contribute significantly to the model. C. For every one year that a person gets older, the lung capacity is expected to increase by 0.555396 units, holding smoker status constant. D. For every one unit increase in smoker status, lung capacity is expected to decrease by 0.648588 units, holding age constant.4) Use computer software to find the multiple regression equation. Can the equation be used for prediction? A wildlife analyst gathered the data in the table to develop an equation to predict the weights of bears. He used WEIGHT as the dependent variable and CHEST, LENGTH, 4)_ and SEX as the independent variables. For SEX, he used male-1 and female=2. WEIGHT CHEST LENGTH SEX 344 45.0 67.5 1 416 54.0 72.0 1 220 41.0 70.0 360 49.0 68.5 332 44.0 73.0 1 140 32.0 63.0 436 48.0 72.0 1 132 33.0 61.0 356 48.0 64.0 150 35.0 59.0 1 202 40.0 63.0 365 50.0 70.5 1 A) WEIGHT = 196 + 2.35CHEST + 3.40LENGTH + 25SEX; Yes, because the R2 is high. B) WEIGHT =-320+10.6CHEST + 7.3LENGTH-10.7SEX; Yes, because the P-value is high. C) WEIGHT =-442.6 + 12.1CHEST + 3.6LENGTH- 23.8SEX; Yes, because the adjusted R² is high. D) WEIGHT = 442.6+ 12.1CHEST + 4.2LENGTH– 21SEX; Yes, because the P-value is low. %3D |D %3DThe equation of the line containing the points (−2,−4) and (2,5) is y=2.25x+0.5. Compute the sum of the squared residuals of the given data set for this line. The sum of the squared residuals for the line containing the points (−2,−4) and (2,5) is
- Find the means of X and Y variables and the coefficient of correlation between them from the ff two regression equations: 2Y-X-50 = 0 3Y-2X-10 = 0A regression was run to determine if for a certain baseball season, winning percentage, y, and on-base percentage, x, are linearly related. The results were: ˆ y =a+bx a=-0.4875 b=2.94 For this baseball season, the lowest on-base percentage was 0.310 and the highest was 0.362. (a) Write the equation of the Least Square Regression line. ˆ y = -0.4875 Correct + 2.94 x (b) Which is a possible value for the correlation coefficient, r? -1.143 1.235 0.72 -0.68 Correct (c) What does the slope mean in the context of this problem? (d) As the on-base percentage increases by 5 percent, the predicted winning percentage increases Correct by 2.94 Incorrect percent. (e) Would it be a good idea to use this model to predict the winning percentage of a team whose on-base percentage is 0.156? Why or why not? (f) Based on this model, what would you expect the winning percentage to be for a team with on-base percentage 0.35? (Round your answer to three decimal places.)The data show the number of felony convictions, in hundreds, and the crime rate, in crimes per 100,000, for seven randomly selected states. For the given data, a. determine the correlation coefficient between the number of felony convictions and the crime rate, (b) find the equation of the regression line, (c) approximate what crime rate can we anticipate in a state that has 12 hundred felony convictions.Felony convictions: 11.4, 8.1, 6.7, 3.4, 2.4, 2.3, 0.4Crime rate/ 100,000: 12, 9.5, 10.4, 9, 4.2, 5.5, 3.3 A. a. r = 0.906 b. y = 3.85x + 0.777 c. 47 B. a. r = 0.906 b. y = 0.777x + 3.85 c. 13.2 C. a. r = -0.906 b. y = 0.777x - 3.85 c. 5.5 D. a. r = -0.906 b. y = -0.777x + 3.85 c. 5.5
- The electric power consumed each month by a chemical plant is thought to be related to the average ambient temperature ( x1 ), the number of days in the month ( x2 ), the average product purity ( x3 ), and the tons of product produced ( x4 ). The past year’s historical data are available and are presented in the following table:regression model is y = -102.7132 + 0.6054X1 + 8.9236X2 + 1.4374 X3 + 0.0136X4 a) Estimate sigma^2b.) Using ANOVA, test for significance of regression using α=0.05. Determine the critical value of the test statistic (2 decimal places only). c.) Using ANOVA, test for significance of regression using α=0.05. Determine the computed value of the test statistic d) Calculate R^2 for the computed regression model. Express your answer as a number less than 1 (NOT in %). e) Calculate R_adj^2 for the computed regression model. Express your answer as a number less than 1 (NOT in %).f) Test the significance of x3 at α=0.05. Determine the value of the test statistic. g)…Might we be able to predict life expectancies from birthrates? Below are bivariate data giving birthrate and life expectancy information for each of twelve countries. For each of the countries, both x, the number of births per one thousand people in the population, and y, the female life expectancy (in years), are given. Also shown are the scatter plot for the data and the least-squares regression line. The equation for this line is y=82.25 -0.48x. ^ Birthrate, x (number of births per 1000 people) 35.5 44.9 29.7 19.9 13.7 27.0 51.9 15.0 50.9 49.7 39.6 24.4 Send data to calculator Send data to Excel Female life expectancy, y (in years) 67.9 57.9 61.7 71.4 72.5 73.5 55.4 76.5 58.2 60.6 64.4 74.4 Based on the sample data and the regression line, complete the following. Female life expectancy (in years) 85 80+ 75+ 70- 65+ 60- 55+ 50 x X x ++ 10 15 20 25 (b) According to the regression equation, for an increase of one (birth per 1000 people) in birthrate, there is a corresponding decrease…Might we be able to predict life expectancies from birthrates?Below are bivariate data giving birthrate and life expectancy information for each of twelve countries. For each of the countries, both x, the number of births per one thousand people in the population, and y, the female life expectancy (in years), are given. Also shown are the scatter plot for the data and the least-squares regression line. The equation for this line is Ŷ=82.24-0.48x (The 2nd picture contains the rest of the data as it would not fit in the first pic and it includes the question as well.) .