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- Consider the following simple linear regression model: y = β0 + β1x + u. Using a sample of n observations on x and y, you estimate the model by OLS and obtain the estimates βˆ 0, βˆ 1, and the R-squared of the regression, R2 . Then you scale this sample by a factor of 100, obtain a new sample {xi/100; yi/100} for i = 1, . . . , n, re-estimate the model by OLS, and denote the new coefficient estimates by β˜ 0, β˜ 1, and the new R-squared of the regression by R˜2 . a) Give the expression of β˜ 1 in terms of βˆ 1, and justify your answer.Use Least Square Regression to fit y=ax^b to the given below.For x={1 2 3 4 5} and y={2 1 4 3 6} use normal equation (c =(ATA)-1ATy) to find with: a-) linear regression coefficients, b-) the linear regression equation, c-) residel sum of squares(RSS)
- The following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).ŷ = 30 + 0.7x1 + 3x2Also provided are SST = 1200 and SSE = 384.The yearly income of a 24-year-old female individual is _____.A surgery intern has conducted a study of the sleeping habits of her colleagues and has developed a following regression equation: y-hat = 6 + 0.1X, where X is the number of hours working on one shift, and Y is the number of hours sleeping at night after that shift. Yvette worked 10 hours and slept 8 hours. What is Yvette’s residual? 0.1 1 6 7You study the relation between the log excess return on stock XYZ, denoted by Re XY Z,t, and the log excess return on the market portfolio, Re M,t, based on 193 monthly observations: R e XY Z,t = β1 + β2 R e M,t + uXY Z,t. You run this regression in R and obtain from the standard regression output the following parameter estimates and p-values (in squared brackets): Re XY Z,t = −0.3199 + 2.0262 Re M,t + uXY Z,t. [0.7689] [0.0001] (1) (a) Which econometric conclusions you can draw from the p-value of the intercept coefficient? In your answer, clearly explain the meaning of the p-value. Further, refer to the role of the significance level in the context of the test of significance approach, i.e., which steps of the test are (not) affected
- A. Identify the regression analyses necessary for testing this initial model. B. What are the direct and indirect effects of z2 on z5?Find the linearization of ƒ(x) = 2x at x = 0. Then round its coefficients to two decimal places.The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.7 8.1 6.7 3.3 2.7 2.3 2.2 0.3 yy 13.8 10.7 9.9 6.6 6.1 5.9 6.1 4.5 xx = thousands of automatic weaponsyy = murders per 100,000 residents Determine the regression equation in y = ax + b form and write it below. (Round to 2 decimal places) A) How many murders per 100,000 residents can be expected in a state with 6.4 thousand automatic weapons? Answer = Round to 3 decimal places. B) How many murders per 100,000 residents can be expected in a state with 6.7 thousand automatic weapons? Answer = Round to 3 decimal places.
- Identify the assumption(s) of linear regression that is (are) violated in each of the following residual plots.Which of the following does not need to be computed to determine a simple regression line? SSx SP "Y-hat" SSyThe following table contains data for the number of bacteria y (in millions) growing in a particular medium after x hours. Using a calculator or statistical software, find the linear regression line for the data in the table. Enter your answer in the form y=mx+b, with m and b both rounded to two decimal places. x y 0 3.67 1 5.24 2 7.04 3 10.31 4 9.83 5 11.04 6 14.68 7 15.02