Ising the principle of least-squares Fit curve of the form y=acl+b*) to the given data be lowi- 15 Do
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- Is the number of games won by a major league baseball team in a season related to the team's batting average? Data from 14 teams were collected and the summary statistics yield: Ey = 1,134 x= 3.642, =93,110, = 948622, and Txy = 295.54 Find the least squares prediction equation for predicting the number of games won, y, using a straight-line relationship with the team's batting average, x.Design a 3rd order Least-squares function approximation to interpolate between the mid between (2n and 3") for a dataset as chosen by you. Compute the LS model error.Select all the statements that are true of a least-squares regression line. In the equation of the least-squares regression line, ?̂ y^ is a predicted value when ?x is known. The regression line is used to predict ?y from any value of ?x. The regression line maximizes the residuals between the observed values and the predicted values. The coefficient of determination, ?2,r2, measures how much of the variation in the ?y-values is explained by the regression line. The slope of the regression line is resistant to outliers. The sum of the squares of the residuals is the smallest sum possible.
- A researcher wishes To determine the relationship between the number of Cows(in thousands) in counties in southwestern Pennsylvania and the milk production ( in millions of pounds.) After computing the least squares regression line, it is determined that r^2=0.9972. Which of the following is the correct interpretation of this value? Answer Choices: A.) none of the other answers is a correct interpretation B.) About 99.72% of the changes in the number of cows are explained by changes in milk production C.) About 99.72% of the change in milk production are explained by changes in the number of cows.Describe Multivariate Gaussian and Weighted Least Squares.Lulu Hypermarket has a record showing data on sales per year (in thousands of rials) and advertisement (in hundreds of rials) for the last five years. The record gives the following details. EX = 132 ΣΧ3,502 EY = 96 EY² = 1,870 ΣΧΥ-2,553 a. Please develop the least squares estimated regression line. b. Using your regression line developed in Part a, predict the sales when advertisement is $3,000. c. At a = 0.05, determine if advertisement and sales are related (perform a t test). d. Develop a 95% confidence interval for estimating the mean sale for those years when advertisement was $3,000. e. Compute the coefficient of determination. ||
- A collection of paired data consists of the number of years that students have studied Spanish and their scores on a Spanish language proficiency test. A computer program was used to obtain the least squares linear regression line and the computer output is shown below. Along with the paired sample data, the program was also given an x value of 2 (years of study) to be used for predicting te For a person who studies for 2 years, obtain the 95% prediction interval and write a statement interpreting the interval. (42.72, 63.98); We can be 95% confident that the test score of an individual who studies 2 years will lie in the interval (42.72, 63.98) (31.61, 75.09); We can be 95% confident that the test score of an individual who studies 2 years will lie in the interval (31.61, 75.09) (42.72, 63.98); We can be 95% confident that the mean test score of all individuals who study 2 years will lie in the interval (42.72, 63.98) (31.61, 75.09); We can be 95%…Each of 25 teenage girls with one brother was asked to provide her own height (y), in inches, and the height (x), in inches, of her brother. The scatterplot below displays the results. Only 22 of the 25 pairs are distinguishable because some of the (x,y) pairs were the same. The equation of the least-squares regression line is ŷ = 35.1 + 0.427x.*Girls are on the y-axis and brothers are on the x-axis* a.) Draw the least-squares regression line on the scatterplot above. b.) One brother’s height was x = 67 inches and his sister’s height was y = 61 inches. Circle the point on the scatterplot above that represents this pair and draw the segment on the scatterplot that corresponds to the residual for it. Give a numerical for the residual. c.) Suppose the point x = 84 , y = 71 is added to the data set. Would the slope of the least squares regression line increase, decrease, or remain about the same?Explain. Would the correlation increase, decrease, or remain about the same? Explain.Consider the data points (2,7) and (3,4). (a) Find the straight line that provides the best least-squares fit to these data. (b) Use the slope and point-slope form to find the equation of the straight line passing through the two points. (c) Explain why it could have been predicted that the straight line in (b) would be the same as the straight line (a)
- State the least squares criterion, Q.Explain the Extended Least Squares Assumptions?The output table below represents the results of the estimation of household expenditures (Y) and income (X) in thousand dollars. Considering the results, answer the following questions. Dependent Variable: Y Method: Least Squares Date: 01/07/16 Time: 11:22 Sample: 2000 2015 Included observations: 16 Variable Coefficient Std. Error t-Statistic Prob. C -0.241942 2.452237 -0.098662 0.9228 X 0.363176 0.013890 26.14674 0.0000 R-squared 0.979933 Mean dependent var 55.43750 Adjusted R-squared 0.978499 S.D. dependent var 33.17221 S.E. of regression 4.864079 Akaike info criterion 6.118100 Sum squared resid 331.2297 Schwarz criterion 6.214674 Log likelihood -46.94480 Hannan-Quinn criter. 6.123046 F-statistic 683.6522 Durbin-Watson stat 0.632113…
