6. Determine the equation, which will represent the best line for the following set of data and solve for the unknown variables as listed below the table. Method of Least Squares X 0 1 2 3 4 5 6 1 2 3 4 5 6 7 8 9 10 789 y 4.6 7.1 9.5 11.5 13.7 15.9 18.6 20.9 23.5 25.4 XX 0 1 4 9 16 25 36 49 64 81 xy 0 7.1 19.0 34.5 54.8 79.5 111.6 146.3 188.0 228.6
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- Given are five observations for two variables, x and y. xi 3 8 12 18 20 yi 54 57 50 24 11 -select your answer choices- b. The least squares line provided an (good, bad) fit; __ % of the variability in y has been explained by the estimated regression equation (to 1 decimal)The following table shows the length, in centimeters, of the humerus and the total wingspan, in centimeters, of several pterosaurs, which are extinct flying reptiles. (A graphing calculator is recommended.) (a) Find the equation of the least-squares regression line for the data. (Where × is the independent variable.) Round constants to the nearest hundredth. y= ? (b) Use the equation from part (a) to determine, to the nearest centimeter, the projected wingspan of a pterosaur if its humerus is 52 centimeters. ? cmGiven are five observations for two variables, x and y. xi 5 9 13 17 20 yi 50 54 46 23 11 The estimated regression equation for these data is ŷ=0.6+2.6x a. Compute SSE, SST, and SST (to 2 decimals) and show work. SSE=________ SST=_________ SSR=_________ b.Compute the coefficient of determination r^2. Comment on the goodness of fit. The least squares line provided a good fit; ________% of the variability in y has been explained by the estimated regression equation (to 3 decimal). Show work. c. Compute the sample correlation coefficient. Enter negative value as negative number. Show work. ___________________
- An agent for a residential real estate company in a large city would like to be able to predict the monthly rental cost for apartments, based on the size of an apartment, as defined by square footage. The agent selects a sample of 25 apartments in a particular residential neighborhood and gathers the following data a. Construct a scatter plot. b. Use the least-squares method to determine the regression coefficients b0 and b1 c. Interpret the meaning of and in this problem. d. Predict the monthly rent for an apartment that has 1,000 square feetThe regional transit authority for a major metropolitan area wants to determine whetherthere is any relationship between the age of a bus and the annual maintenance cost. Asample of 10 buses resulted in the following data. Age of Bus (year) Maintenance Cost ($) 1 350 2 370 2 480 2 520 2 590 3 550 4 750 4 800 5 790 5 950 a. Develop the least squares estimated regression equation.b. Test to see whether the two variables are significantly related with α = .5.c. Did the least squares line provide a good fit to the observed data? Explain.d. Develop a 95% prediction interval for the maintenance cost for a specific bus thatis 4 years old.A researcher collected data on the cholesterol level, CC, and the age, AA, of 24 people selected at random. Using the data, the researcher calculated the least-squares regression line to be Cˆ=182+2.2AC^=182+2.2A and the standard error of the slope to be 0.38. If the conditions for inference are met, which of the following is closest to the value of the test statistic to test the hypotheses H0:β=0H0:β=0 versus Ha:β≠0Ha:β≠0 ?
- Given are five observations for two variables, x and y. x 1 2 3 4 5 y 3 7 7 10 15 The estimated regression equation for these data is y=0.3+2.7x. a. Compute SSE, SST, and SSR using the following equations (to 1 decimal). SSE SST SSR b. Compute the coefficient of determination r^2 (to 3 decimals). Does this least squares line provide a good fit? - Select your answer -Yes, the least squares line provides a very good fit No, the least squares line does not produce much of a fit c. Compute the sample correlation coefficient (to 4 decimals).Given are five observations for two variables, and . Xi 1 2 3 4 5 Yi 4 7 7 12 14 The estimated regression equation for these data is yhat = 1.3+2.5x. a. Compute SSE, SST, and SSR using the following equations (to 1 decimal). SSE SST SSR b. Compute the coefficient of determination rsquare (to 3 decimals). Does this least squares line provide a good fit? - Select your answer -No, the least squares line does not produce much of a fitYes, the least squares line provides a very good fitItem 5 c. Compute the sample correlation coefficient (to 4 decimals).Which method gives a unique set of values to the constants in the equation of the fitting curves? * Newton's Method Interpolation Horner’s method Method of least squares
- 2. A company that holds the DVD distribution rights to movies previously released only in theaters wants to estimate sales revenue of DVDs based on box office success. The box office gross (in Php millions) for each of 22 movies in the year that they were released and the DVD revenue (in Php millions) in the following year are shown below and stored in (pic) a. construct a scatter plot. b. assuming a linear relationship, use the least-squares method to determine the regression coefficients b0 and b1.A pediatrician wants to determine the relationship that exists between achild’s height, x, and head circumference, y. She randomly selects 11 children from her practice, measures their heights and head circumferences, and conducts the least-squares regression analysis with the simple linear model using StatCrunch. The output is given below: (a) Write down the equation of the least-squares regression line treating height as the explanatory variable and head circumference as the response variable. (b) Interpret the slope and y-intercept, if appropriate. (c) Use the regression equation to predict the head circumference of a child who is 25 inches tall. Assume that the regression model is applicable.(d) It is observed that one child who is 25 inches tall has a head circumference of 17.5 inches. Is the observed value above or below average among all children with heights of 25 inches?The following table shows the marks in statistics and economics for ten students. Fit a least square line to the data using a) ‘X’ as the independent variable b) What will be the regression equation if X= 20