The following data were collected during a study of consumer buying patterns: Observation Observation 1. 18 69 19 81 2. 26 81 14 75 41 85 10 10 76 4. 35 77 11 25 83 56 95 12 21 86 46 93 13 29 90 33 86 Click here for the Excel Data File b. Obtain a linear regression line for the data (Round your intermediete calculations and final answers to 3 decimal pleces.) y3=

Analysts at a start-up company are analyzing 35 months of sales data. They partition the data (the first 20 observations are assigned to the training set; the most recent 15 months are in the test set). The only independent variable is T (month number, ranging from 1 to 35). Five models (polynomials of order 1 - 5) are fit to the data. The first order is just the linear model; the 2nd order polynomial is the quadratic model; order 3 is the cubic model, etc. In each case the model is fit on the training data, and scored on both the training and test data sets. The results are below. Based on this output, which is the best predictive model? Metrics AE RMSE MAE SSE Metrics AE RMSE MAE SSE Model 2 Model 3 Model 5 Model 4 Model 1 1 <0.000001 0.955978 0.792802 18.277907 1 -1.034550 1.424155 1.208991 30.423248 Training Data Scoring Models (Polynomial of order 1-5) 4 2 <0.000001 0.928791 0.759583 17.253086 3 <0.000001 <0.000001 0.928295 0.855568 0.761951 0.652212 17.234646 14.639962 Test Data…

We  use  the  Breast  Cancer  Wisconsin  dataset  from  UCI  machine  learning  repository: http://archive.ics.uci.edu/ml/datasets/Breast+Cancer+Wisconsin+%28Diagnostic%29 Data File: breast-cancer-wisconsin.data (class: 2 for benign, 4 for malignant) Data Metafile: breast-cancer-wisconsin.names  Please  implement  this  algorithm  for  logistic  regression  (i.e.,  to  minimize  the  cross-entropy loss as discussed in class), and run it over the Breast Cancer Wisconsin dataset. Please  randomly  sample  80%  of  the  training  instances  to  train  a  classifier  and  then testing it on the remaining 20%. Ten such random data splits should be performed and the average over these 10 trials is used to estimate the generalization performance. You  are  expected  to  do  the  implementation  all  by  yourself  so  you  will  gain  a  better understanding of the method. Please submit: (1) your source code (or Jupyter notebook file) that TA should be able to (compile  and) run, and the…

A Ridge Linear Regression adds the sum of the squared values of the coefficients to the loss function to penalize large coefficients.   Group of answer choices True False

In the simple linear regression equation ŷ = bo + b₁x, how is b₁ interpreted? it is the change in that occurs with a one-unit change in y O It is the estimated value of ŷ when x = 0 O It is the change in ŷ that occurs when bo increases O it is the change in ŷ that occurs with a one-unit change in

The first principal component is a normalized linear combination of the original variables with the largest varianceTrueFalse

Assume the following simple regression model, Y = β0 + β1X + ϵ ϵ ∼ N(0, σ^2 )   Now run the following R-code to generate values of σ^2 = sig2, β1 = beta1 and β0 = beta0. Simulate the parameters using the following codes:   Code:   # Simulation ##  set.seed("12345")  beta0 <- rnorm(1, mean = 0, sd = 1) ## The true beta0  beta1 <- runif(n = 1, min = 1, max = 3) ## The true beta1  sig2 <- rchisq(n = 1, df = 25) ## The true value of the error variance sigmaˆ2    ## Multiple simulation will require loops ##  nsample <- 10 ## Sample size n.sim <- 100 ## The number of simulations  sigX <- 0.2 ## The variances of X #   # Simulate the predictor variable ##  X <- rnorm(nsample, mean = 0, sd = sqrt(sigX))   Q1  Fix the sample size nsample = 10 . Here, the values of X are fixed. You just need to generate ϵ and Y . Execute 100 simulations (i.e., n.sim = 100). For each simulation, estimate the regression coefficients (β0, β1) and the error variance (σ 2 ). Calculate the mean of…

The following dataset is a historic record of 14 houses that were sold in a small town in BC. The dataset is used to predict whether a new house in the same town will be sold in 10 days if listed with a specific price based on certain attributes. We are considering only four attributes (price, number of bedrooms, size, and distance to bus stop) just to simplify the calculations in this assignment but more attributes should be considered in real applications. House Price Number of Bedrooms Size (sqft) Distance to Bus-Stop House sold in 10 days? House 1 $300,000 1 3,500 sqft far No House 2 $300,000 1 3,500 sqft near No House 3 $250,000 1 3,500 sqft far Yes House 4 $350,000 2 3,500 sqft far Yes House 5 $350,000 3 5,000 sqft far Yes House 6 $350,000 3 5,000 sqft near No House 7 $250,000 3 5,000 sqft near Yes House 8 $300,000 2 3,500 sqft far No House 9…