a)
when Y is regressed on X
then slope =
when X is regressed on Y
product =
hence
m1 m2 is same as shown in image
b)
here m1m2 >= 0
for perpendicular
m1 m2 should be -1
hence two lines will never be perpendicular
Q6). Suppose that you want to fit two separate regression lines on the same data set - For the first least square fit, Y is the response variable and X is the predictor variable For the second le...
Q7). Let y,,y.., y represent the life time for the computer chips that are exponentially distributed with pdf e^ for else (a). Derive the likelihood ratio test for testing Ho: λ A, versus Ha: λ> λ (b). If a random sample of life times for the computer chips are 4 years, 5 years, 7 years, 6 years, 7 years, Use α-005 does this sample support the fact that λ > 4.5 years ?. 4.6, 4.7, 4.8, 4.9, 5.0 Compute the...
Here is a bivariate data set. Find the regression equation for the response variable y. x y 53.6 37 63.5 52.6 56.2 40.5 95.3 73.3 31.4 13.3 52.9 26.3 61.6 48.7 62.6 46.5 55.7 34.2 48.6 26.9 56.7 38.2 42.4 22.5 61.6 46.3 35.1 25.2 90.3 71.7 78.1 48.6 72.8 54.6 regression equation: Enter the equation in slope-intercept form with parameters accurate to three decimal places.
Question 5. Given sample data (x, y), and sample size n. We fit the simple regression model: and estimate the least square estimators (a) Suppose A,-1, ß,-2, and x-1. Compute у. b) Suppose S and sry 0.5, compute the R2. Question 5. Given sample data (x, y), and sample size n. We fit the simple regression model: and estimate the least square estimators (a) Suppose A,-1, ß,-2, and x-1. Compute у. b) Suppose S and sry 0.5, compute the R2.
Find the least squares regression line for the data points. (Let x be the independent variable and y be the dependent variable.) Graph the points and the line on the same set of axes 3 -3 3 -3 Find the least squares regression line for the data points. (Let x be the independent variable and y be the dependent variable.) Graph the points and the line on the same set of axes 3 -3 3 -3
1. Choose a data set of your own:?Response or dependent variable (Y)?At least 3 or more independent variables (X1, X2, X3, ... etc.) that you believe has an influence on Y.?At least 40 observations or data points?If there are categorical variables, model them appropriately2. Fit a multiple regression model. ?Interpret the model equation?Are all the chosen variables significant? Discuss.?Check for model assumptions and make appropriate comments.?How good is the model? Comment on R2 , R , se, F-value etc and...
Question text Suppose that you have a five-point sample data set; the observations of (x, y) are given by (8, 3), (10, 3), (6, 2), (2, 0), and (2, 1). Fit a simple linear regression model to this data by first computing the least squares estimate of the slope parameter. Which of the following is the most accurate? Select one: a. 0.3438 b. 0.4728 d. 0.6712
(a) Suppose you are given the following (x, y) data pairs x136y217Find the least-squares equation for these data (rounded to three digits after the decimal) (b) Now suppose you are given these (x, y) data pairs. x217y136Find the least-squares equation for these data (rounded to three digits after the decimal). (c) In the data for parts (a) and (b), did we simply exchange the x and y values of each data pair? Yes No (d) Solve your answer from part (a) for x (rounded to...
Homework 4 Use the hand span data that we collected in class for homework Suppose you want to buy someone a pair of love, but you do not know their love size. Usually, we do have a pretty good idea of the person's height. Let' asume that the right hand span is a rood indicator of the love size. So let find the best predictor of right hand span be on the person's height. Once we can predict the right...
X Part I. Derive Bivariate Regression by hand. Again, we are using the same data set that we used in the in-class assessment. Case Dietary Fat Body Fat 22 9.8 22 11.7 14 8.0 21 9.7 32 10.9 26 7.8 30 21 17 1. Step 1: Find the mean of dietary fat x = 2. Step 2: Find the mean of body fat y = 3. Step 3: Find the sum of (x1 - x)y- y) = 3316 4. Step...
1. For each of the following regression models, write down the X matrix and 3 vector. Assume in both cases that there are four observations (a) Y BoB1X1 + B2X1X2 (b) log Y Bo B1XiB2X2+ 2. For each of the following regression models, write down the X matrix and vector. Assume in both cases that there are five observations. (a) YB1XB2X2+BXE (b) VYBoB, X,a +2 log10 X2+E regression model never reduces R2, why 3. If adding predictor variables to a...