For the model y, = B₁ + B₁x, + ε₁ ; ɛ, ~ N(0,2), the following statistics are computed: 9 x₁ =0 9 y₁ = 0 i=1 x=324 i=1 =324 i=1 Στιν x,y,243 (a) Compute the least squares estimates, B. and B (b) Compute SSE, SST, and R2 (c) Compute a 95% confidence interval for B (d) Use the confidence interval method and test the following hypothesis test (a=0.05) Ho B₁ =0 H₁: B₁ = 0
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- Compute the sum of squares error (SSE) by hand for the given set of data and linear model: (6,6),(7,7),(8,9); Y = x - 1Consider the following data set : (x, y) : (1.0, 5.1), (1.25, 5.79), (1.5, 6.53), (1.75, 7.45), (2.0, 8.46) If the least squares approximation of the form beax is y=(3.07) e(0.5056)x then the total error is: Select one: a. 0.015 O b. 1.150 O c. 0.0015 O d. 0.150EXER 5.1: Given the observations (1,1), (2,3), (4,5), find the least squares estimates for m and b for the best fit line y=mx+b.
- Find the least squares approximating line y = 20 21 for the following sets of data points. What is the value forz1? (1, 0), (2, 2), (3, 3), (4, 6) -1.9 2.9 -2.9 1.9A regression analysis between demand (y in Kg) and supply (x in kg) resulted in the following least squares line: = 50 - 15 X.Find the least squares line y = ß1 + B2x that best fits the data points (0, 1), (2,0), (3, 1), (5, –1). What is the least squares error?
- Consider the points (1, 1), (2, 3), (−3, 1). Find the least squares regression line.Fit a curve of the form g(x) = A10Bx to the dataset using the Least Squares Method. Calculate the corrected values and the total squared error.Consider the data points (1, 0), (2, 1), and (3, 5). Compute the least squares error for the given line. In each case, plot the points and the line. y= -3 + 5/2 x
- 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. ||The model, y = Bo + B₁×1 + ß₂×₂ + ε, was fitted to a sample of 33 families in order to explain household milk consumption in quarts per week, y, from the weekly income in hundreds of dollars, X₁, and the family size, x2. The total sum of squares and regression sum of squares were found to be, SST = 162.1 and SSE(R) = 90.6. The least squares estimates of the regression parameters are bo = -0.022, b₁ = 0.051, and b₂ = 1.19. A third independent variable number of preschool children in the household-was added to the regression model. The sum of squared errors when this augmented model was estimated by least squares was found to be 83.1. Test the null hypothesis that, all other things being equal, the number of preschool children in the household does not affect milk consumption. Use α = 0.01. Click here to view page 1 of a table of critical values of F. Click here to view page 2 of a table of critical values of F. Choose the correct null and alternative hypotheses below. A. Ho: B3 = 0 |…The model, y = Bo + B₁×₁ + ß₂×2 + ε, was fitted to a sample of 33 families in order to explain household milk consumption in quarts per week, y, from the weekly income in hundreds of dollars, x₁, and the family size, x₂. The total sum of squares and regression sum of squares were found to be, SST = 162.1 and SSE(R) = 90.6. The least squares estimates of the regression parameters are bo = -0.022, b₁ = 0.051, and b₂ = 1.19. A third independent variable-number of preschool children in the household-was added to the regression model. The sum of squared errors when this augmented model was estimated by least squares was found to be 83.1. Test the null hypothesis that, all other things being equal, the number of preschool children in the household does not affect milk consumption. Use α=0.01. Click here to view page 1 of a table of critical values of F. Click here to view page 2 of a table of critical values of F. ''1' M P2 P3 Find the critical value. The critical value is 7.60⁰. (Round to…