Find the least square estimate for beta (the slope) given that its y-intercept is 0. Y_i = BetaX_i + e_i where e_i are independent and identically distributed N(0, variance_e) randon variables i = 1,...,2.
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- Curing times in days (x) and compressive strengths in MPa (V) were recorded for several concrete specimens. The means and standard deviations of the x and y values were * = 5, s, = 2, 5 = 1350, s, = 100. The correlation between curing time and compressive strength was computed to be r = 0.7. Find the equation of the least-squares line to predict compressive strength from curing time.A regression and correlation analysis resulted in the following information regarding a dependent variable (y) and an independent variable (x). Σx = 90 Σ(y - )(x - ) = 466 Σy = 170 Σ(x - )2 = 234 n = 10 Σ(y - )2 = 1434 SSE = 505.98 The least squares estimate of the slope or b1 equals a. .923. b. 1.991. c. -1.991. d. -.923.The least squares regression line for a set of data is calculated to be y = 24.8 + 3.41x. (a) One of the points in the data set is (4, 37). Calculate the predicted value. (b) For the point in part (a), calculate the residual.
- Two variables have the regression lines 3x + 2y = 26 and 6x + y = 31. Find the mean values, the correlation coefficient between x and y and the ratio of variances of the variables.Interpret the least squares regression line of this data set. Meteorologists in a seaside town wanted to understand how their annual rainfall is affected by the temperature of coastal waters. For the past few years, they monitored the average temperature of coastal waters (in Celsius), x, as well as the annual rainfall (in millimetres), y. Rainfall statistics • The mean of the x-values is 11.503. • The mean of the y-values is 366.637. • The sample standard deviation of the x-values is 4.900. • The sample standard deviation of the y-values is 44.387. • The correlation coefficient of the data set is 0.896. The correct least squares regression line for the data set is: y = 8.116x + 273.273 Use it to complete the following sentence: The least squares regression line predicts an additional annual rainfall if the average temperature of coastal waters increases by one degree millimetres of Celsius.Use the least squares regression line of this data set to predict a value. Meteorologists in a seaside town wanted to understand how their annual rainfall is affected by the temperature of coastal waters. For the past few years, they monitored the average temperature of coastal waters (in Celsius), x, as well as the annual rainfall (in millimetres), y. Rainfall statistics • The mean of the x-values is 11.503. • The mean of the y-values is 366.637. • The sample standard deviation of the x-values is 4.900. • The sample standard deviation of the y-values is 44.387. • The correlation coefficient of the data set is 0.896. The least squares regression line of this data set is: y = 8.116x + 273.273 How much rainfall does this line predict in a year if the average temperature of coastal waters is 15 degrees Celsius? Round your answer to the nearest integer. millimetres
- a. Show that the regression R2 in the regression of Y on X is the squaredvalue of the sample correlation between X and Y. That is, show thatR2 = r2XY.b. Show that the R2 from the regression of Y on X is the same as the R2from the regression of X on Y. c. Show that ^β1 = rXY (sY/sX), where rXY is the sample correlationbetween X and Y, and sX and sY are the sample standard deviationsof X and Y.Two regression lines of a sample are X+6 Y=6 and 3X+2Y=0. Find the correlation coefficient.Use the following data for parts (a) through (e). x 5 7 3 16 12 9 y 8 9 11 27 15 13 Determine the equation of the least squares regression line to predict y by x. y^ = (value rounded to 4 decimal places ?) + (value rounded to 4 decimal places ?) x
- Find the equation for the least squares regression line of the data described below. Meteorologists in a seaside town wanted to understand how their annual rainfall is affected by the temperature of coastal waters. For the past few years, they monitored the average temperature of coastal waters (in Celsius), x, as well as the annual rainfall (in millimetres), y. Rainfall statistics • The mean of the x-values is 11.503. • The mean of the y-values is 366.637. • The sample standard deviation of the x-values is 4.900. • The sample standard deviation of the y-values is 44.387. • The correlation coefficient of the data set is 0.896. Round your answers to the nearest thousandth. y = L SubmitCompute the least-squares regression line for predicting y from x given the following summary statistics. Round the slope and y-intercept to at least four decimal places. x = 12.5 sx = 2.2 y = 1400 sy = 1.8 r = 0.50 Regression line equation: y^ = ___. image attached bellow for better view.A set of n = 25 pairs of X and Y values has a correlation of r = -0.50 with SSX = 38 and SSY = 14. Find the standard error of estimate for the regression equation. What percentage of the variance in Y is accounted for by X?