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1. For each of the following regression models, write down the X matrix and 3 vector....
The Motor Trend Car Road Tests dataset mtcars, in faraway R package, was extracted from the 1974 Motor Trend US magazine, and comprises fuel consumption and 10 aspects of automobile design and performance for 32 automobiles (1973–74 models). The data frame has 32 observation on 11 (numeric) variables: mpg: Miles/(US) gallon; cyl: Number of cylinders; disp: Displacement (cu.in.); hp: Gross horsepower; drat: Rear axle ratio; wt: Weight (1000 lbs); qsec: 1/4 mile time; vs: Engine (0 = V-shaped, 1 =...
The data set "mtcars" in R has 11 variables with 32 observations. A data frame with 32 observations on 11 variables. [, 1] mpg Miles/(US) gallon [, 2] cyl Number of cylinders [, 3] disp Displacement (cu.in.) [, 4] hp Gross horsepower [, 5] drat Rear axle ratio [, 6] wt Weight (1000 lbs) [, 7] qsec 1/4 mile time [, 8] vs V/S [, 9) am Transmission (0 = automatic, 1 = manual) [,10] gear Number of forward gears...
Answer the following question by showing the codes in R 2. Consider the dataset mtcars and suppose we are interested in modeling the mpg of a vehicle based on a single variable presented in the dataset. a) Use the cor ) function in R, apply it to only numerical variables in the dataset. Identify the numerical variable that shows the most significant correlation, and generate a scatterplot between this variable and mpg. b) Use the 1m() function in R to...
PLEASE ANSWER ALL parts . IF YOU CANT ANSWER ALL, KINDLY ANSWER PART (E) AND PART(F) FOR PART (E) THE REGRESSION MODEL IS ALSO GIVE AT THE END. REGRESSION MODEL: We will be returning to the mtcars dataset, last seen in assignment 4. The dataset mtcars is built into R. It was extracted from the 1974 Motor Trend US magazine, and comcaprises fuel consumption and 10 aspects of automobile design and performance for 32 automobiles (1973-74 models). You can find...
2. What is the coefficient of correlation between miles per gallon and weight? What is the sign of the correlation coefficient? Does the coefficient of correlation indicate a strong correlation, weak correlation, or no correlation between the two variables? How do you know? See Step 3 in the Python script. 3. Write the simple linear regression equation for miles per gallon as the response variable and weight as the predictor variable. How might the car rental company use this model?...
Considering multiple linear regression models, we compute the regression of Y, an n x 1 vector, on an n x (p+1) full rank matrix X. As usual, H = X(XT X)-1 XT is the hat matrix with elements hij at the ith row and jth column. The residual is e; = yi - Ýi. (a) (7 points) Let Y be an n x 1 vector with 1 as its first element and Os elsewhere. Show that the elements of the...
Considering multiple linear regression models, we compute the regression of Y, an n x 1 vector, on an n x (p+1) full rank matrix X. As usual, H = X(XT X)-1 XT is the hat matrix with elements hij at the ith row and jth column. The residual is e; = yi - Ýi. (a) (7 points) Let Y be an n x 1 vector with 1 as its first element and Os elsewhere. Show that the elements of the...
The standard linear regression model is: y = Xw+e, where X is an nxd matrix of predictor vari- ables, y is an n-dimensional vector of response variables, and e N (0,021) is an n-dimensional vector of model errors. (a) What is the PDF of y in terms of X,w, o?? N(0,p1). (b) Let the PDF from part (a) be denoted as fylw). Suppose also in this case that w Write an expression for the joint PDF of w and y...
correlation and regression 210 Statistics EXTRA CREDIT Correlation and Regression Formulas written Assignment 1. Follow the instructions below to calculate the correlation coefficient and least squares regression line for the data set below. Z 22,- The sample means and sample standard deviations for the two variables are listed below: X = 4 x = 2 3 =5 Sy = 1 The linear correlation coefficient is = 52. Calculate this correlation coefficient using the steps below: (a) First, complete the columns...
3. In the multiple regression model shown in the previous question, which one of the following statements is incorrect: (b) The sum of squared residuals is the square of the length of the vector ü (c) The residual vector is orthogonal to each of the columns of X (d) The square of the length of y is equal to the square of the length of y plus the square of the length of û by the Pythagoras theorem In all...