2. Suppose Y ~ Exp(a), which has pdf f(y)-1 exp(-y/a). (a) Use the following R code to generate data from the model Yi...
R STUDIO Create a simulated bivariate data set consisting of n 100 (xi, yi) pairs: Generate n random a-coordinates c from N(0, 1) Generate n random errors, e, from N(0, o), using o 4. Set yiBoB1x; + , Where Bo = 2, B1 = 3, and eN(0, 4). (That is, y is a linear function of , plus some random noise.) (Now we have simulated data. We'll pretend that we don't know the true y-intercept Bo 2, the true slope...
Consider the following data for two variables, x and y. a. Choose the correct scatter diagram with x and y. The correct scatter diagram is - _______ . Does there appear to be a linear relationship between x and y? Explain. The scatter diagram- Select your answer - some evidence of a possible linear relationship. b. Develop the estimated regression equation relating x and y. Save "predicted" and "residuals" (to 4 decimals). c. Choose the correct scatter diagram or the residuals versus y tor the estimated...
3. Consider the following data for two variables, x and y. 4 5 4 6 4 6 9 5 11 a. Does there appear to be a linear relationship between x and y? Explain. b. Develop the estimated regression equation relating x and y. c. Plot the standardized residuals versus g for the estimated regression equation developed in part (b). Do the model assumptions appear to be satisfied? Explain. d. Perform a logarithmic transformation on the dependent variable y. Develop...
Below are given (a) A scatterplot of Y versus X and (b) A plot of residuals versus fitted values after a simple linear regression model was fit to the data. What is the equation of the fitted line? Discuss what is indicated about the relationship between Y and X as it relates to simple linear regression. Fitted Line Plot Y = - 14.64 + 7.431 X R-Sq R-Sq (adj) 2.43700 91.9% 91.8% 1 > 20- 3 4 5 6 7...
1. Consider a GLM (generalised linear model) for a Poisson random sample Y1,. .. , Y, with \Vi each Yi having a pdf or pmf f(y; A;) = i= 1, . .. ,n. Yi = 0, 1,2, -..; ^; > 0; Y;! Note that the pdf from an exponential family has the following general form b(0) + c(y, a(o) y0 exp f(y; 0, 6) = Suppose the linear predictor of the GLM is n = a+Bxi, with (a,B) being the...
1. If a true model of simple linear regression reads: yi −y ̄ = β0 +β1(xi −x ̄)+εi for i = 1, 2, · · · , n, showβ0 =0andβˆ0 =0. (1pt) (hint: use the formula of estimator βˆ0 = y ̄ − βˆ1x ̄.)
Need help with stats true or false questions Decide (with short explanations) whether the following statements are true or false a) We consider the model y-Ao +A(z) +E. Let (-0.01, 1.5) be a 95% confidence interval for A In this case, a t-test with significance level 1% rejects the null hypothesis Ho : A-0 against a two sided alternative. b) Complicated models with a lot of parameters are better for prediction then simple models with just a few parameters c)...
Decide (with short explanations) whether the following statements are true or false. e) In a simple linear regression model with explanatory variable x and outcome variable y, we have these summary statisties z-10, s/-3 sy-5 and у-20. For a new data point with x = 13, it is possible that the predicted value is y = 26. f A standard multiple regression model with continuous predictors and r2, a categorical predictor T with four values, an interaction between a and...
1. (2 points) A research presented data on comprehensive strength x and intrinsic permeability y of various concrete mixes and cures. Summary quantities are: n 14,2y 572, E yi 23,530, Σ Xi-43, Σχ-15742, Σχοϊ-1697.80. Assume that the two variables are related according to the simple linear regression model. Calculate the least squares estimates of the slope and intercept. Estimate σ2 1. (2 points) A research presented data on comprehensive strength x and intrinsic permeability y of various concrete mixes and...
2. R programming 2·The data set prostate in the faraway package is froma study on 97 men with prostate cancer who were due to receive a radical prostatectomy We are interest is in predicting lpsa (log prostate specific antigen) with Icavol (log cancer volume). (a) Draw a scatterplot -does a simple linear regression model seem reasonable? (b) Without using the R function Im), compute the values T,Y, Sxx, Syy and Sxy. Com- pute the ordinary least squares estimates of the...