Statel O None of these O Regression between X and Y determines the natur variables. Regression between X and Y determines whether t

Find the least squares regression line for the data points. (Let x be the independent variable and y be the dependent variable.) (-1, 2), (1, 0), (3, –1) y = -0.75x +1.0833

Statistics

The Simple Linear Regression model is       Y = b0 + b1*X1 + u       and the Multiple Linear Regression model with k variables is:       Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u       Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term,       Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients.   QUESTION 4 Suppose we have an SLR model, where the dependent variable (Y) represents ‘how satisfied someone is with his/her life, from 0 to 100’ (the higher the value, the higher the satisfaction with life), and the explanatory variable (X1) represents ‘personal annual income in £1,000’. The estimated OLS regression line is:  Yhat = 33.2 + 0.74*X1.  According to this model, what is the predicted life satisfaction, for someone with…

What kind of variable is x in terms of linear regression? *   a) Independent   b) Dependent   c) Both of the above   d) None of the above

Consider the regression model Y₁ = BX; +u; Y Where ui and X; satisfy the assumptions specified here. Let ẞ denote an estimator of ẞ that is constructed as ẞ = Show that ẞ is a linear function of Y₁, Y2,..., Yn. Show that ẞ is conditionally unbiased. 1. E (YiX1, X2,..., Xn) = == X + +Yn) 2. E(B|×1, X2,..., Xn) = E = B Χ | (X1, X2,..., Xn) = where Y and X are the sample means of Y; and X;, respectively.

Find the least squares regression line for temperature (x) and number of ice cream cones sold per hour (y). 65 70 75 80 85 90 95 100 105 y 8 10 11 13 12 16 19 22 23 Oŷ = 2.469x+48.240 ý = 0.383x-17.694 Oŷ = -125.376x+31.656 Oŷ = 0.4x-18

Linear regression activity. Tune current between one and six years old were randomly selected from the classified ads of the Arizona republic.The following data were obtained where X donates age in years,and y donates price,in hundreds of dollars. x (age) 6,6,6,2,2,5,4,5,1,4 price(100ths) 270,260,275,405,364,295,335,308,405,305 Draw a scatter diagram. Find the linear correlation coefficientr. describe the shape strength and direction.does a linear relationship exist between the age of Corvette and its price (use the critical value to explain).If appropriate explain the slope in contexts. If appropriate explain the Y intercept in context.Predict the price of a one year old Corvette.Find the residual of a one year old Corvette.

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A6 Assume that least squares regression is used to fit a regression line y = â + 3x to data (xi, yi) for i=1,2,..., n. The sample means of the x, and yi are and y, respectively. The variability of the y, about the regression line equals 2. Which of the following expressions would be a suitable estimate for o²? A: 1 n-1 n i=1 (Yi - y)² D: 1 n - 2 B: 0² Σ=1(x − x)2 n Σ(y - a - βα;)2 i=1 0² n