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4. Consider the following data. 16 74 900 29810 (a) Suppose you would like to fit...
Linear Algebra Question 25. Suppose you are looking at data which is supposed to fit an...
Linear Algebra Question
25. Suppose you are looking at data which is supposed to fit an exponential equation, i.e. a model of the form y= Cekz where C and k are constants. Suppose your data points are (2, 5), (3,8) and (4, 17). Use least-squares to find (decimal approximations to) the values of C and k which best fit this model How to proceed: First, take the natural log of both sides of the model to obtain what is called...
q We would like to fit a line y = cx + d to the following...
q
We would like to fit a line y = cx + d to the following data х у -1 -3 0 -1 0 2 3 using the method of least squares. (a) Write down the (overdetermined) linear system this problem gives rise to in the form Ax = b, where x = (..) (b) Find the best-fit line by computing the least-squares solution of the system Ax = b.
Example 1: Least Squares Fit to a Data Set by a Linear Function. Compute the coefficients of the ...
Example 1: Least Squares Fit to a Data Set by a Linear Function. Compute the coefficients of the best linear least-squares fit to the following data. x2.4 3.6 3.64 4.7 5.3 y| 33.8 34.7 35.5 36.0 37.5 38.1 Plot both the linear function and the data points on the same axis system Solution We can solve the problem with the following MATLAB commands x[2.4;3.6; 3.6;4.1;4.7;5.3]; y-L33.8;34.7;35.5;36.0;37.5;38.1 X [ones ( size (x)),x); % build the matrix X for linear model %...
working under the assumption thata set of data points obeys the exponential (a) Suppose you are...
working under the assumption thata set of data points obeys the exponential (a) Suppose you are model Y, Ae, BX. Derive the linearized model to which we can find a line of best fit (in the least squares sense). 3 marks (b) The lines of best fit for two repetitions of an experiment are reproduced below: Each data set has an obvious outlier. In each case, explain the effect that removing the outlier from the data set will have on...
8. (16 points) Suppose you use a quadratic curve y = ax? +b to fit the...
8. (16 points) Suppose you use a quadratic curve y = ax? +b to fit the three (x,y) points (1,3), (0,-1), (-1,1). Use matrix method as described in class to find the least squares estimate of the constants a and b in the above equation. In particular, formulate the relevant normal equation, whose solution leads to the least squares estimates of a and b, and hence obtain the least squares estimate of a and b.
Linear Algebra To fit data to an exponential model like y = AeKt, we first use...
Linear Algebra
To fit data to an exponential model like y = AeKt, we first use a logarithm to linearize it: . n y n A k t Since A is a constant, so is ln A, and we can write this generically as ln y = co + cit. The table below shows the years different planes were first produced, along with how many displays (gauges, screens, etc.) were present in the cockpit. Year Introduced, y (Year after 1900)...
please answer a) and b) but ignore the matlab part in b) 1. The following data...
please answer a) and b) but ignore the matlab part in
b)
1. The following data represents the bacterial growth in a liquid culture over a number of days x (days) 0 4 8 12 16 20 y (amount=106) 67.38 74.67 82.74 91.69 101.60 112.58 a) Apply linear least-squares regression (by hand) to find the best straight line to fit the data. b) Apply polynomial regression to find the best quadratic polynomial to fit the data. Calcu- late the equations...
This is how you import the Carseats data into Rstudio software: library(“ISLR”) data(“Carseats”) ...
This is how you import the Carseats data into Rstudio
software:
library(“ISLR”)
data(“Carseats”)
view(Carseats)
after that, please provide codes for following:
a. Split the data into a training set and a test set. b. Fit a linear model using least squares on the training set to predict Sales using the entire collection of predictors. Report the Cp, BIC, R2, and RSS for this model c. Use the fitted model to predict responses for the test data and report the test...
9) Suppose you are given n points: (x,y)(, y). And we wish to fit a cirele to the data. A general...
9) Suppose you are given n points: (x,y)(, y). And we wish to fit a cirele to the data. A general circle, as we all know, is Cr-y+-k. So the question becomes: What are h, k, and r so that the circle becomes the best least squares fit? Show that this problem becomes Th .e. What is a, B and what is M? B, When fitting the cirele to the data points (0,2), (1,2),3,-),(0,-D,6,0) what are the normal equations? GIVE...
67. Recently, the annual number of driver deaths per 100,000 for the selected age groups was as follows: Age Number of Driver Deaths per 100,000 16-19 38 20-24 36 25-34 24 35-54 20 55-74 18 75+ 28 Ta...
67. Recently, the annual number of driver deaths per 100,000 for the selected age groups was as follows: Age Number of Driver Deaths per 100,000 16-19 38 20-24 36 25-34 24 35-54 20 55-74 18 75+ 28 Table 12.19 a For each age group, pick the midpoint of the interval for the x value. (For the 75+ group, use 80) b using ages as the independent variable and "Number of driver deaths per 100.000" as the dependent variable, make a...
Linear Algebra Question
25. Suppose you are looking at data which is supposed to fit an exponential equation, i.e. a model of the form y= Cekz where C and k are constants. Suppose your data points are (2, 5), (3,8) and (4, 17). Use least-squares to find (decimal approximations to) the values of C and k which best fit this model How to proceed: First, take the natural log of both sides of the model to obtain what is called...
q
We would like to fit a line y = cx + d to the following data х у -1 -3 0 -1 0 2 3 using the method of least squares. (a) Write down the (overdetermined) linear system this problem gives rise to in the form Ax = b, where x = (..) (b) Find the best-fit line by computing the least-squares solution of the system Ax = b.
Example 1: Least Squares Fit to a Data Set by a Linear Function. Compute the coefficients of the best linear least-squares fit to the following data. x2.4 3.6 3.64 4.7 5.3 y| 33.8 34.7 35.5 36.0 37.5 38.1 Plot both the linear function and the data points on the same axis system Solution We can solve the problem with the following MATLAB commands x[2.4;3.6; 3.6;4.1;4.7;5.3]; y-L33.8;34.7;35.5;36.0;37.5;38.1 X [ones ( size (x)),x); % build the matrix X for linear model %...
working under the assumption thata set of data points obeys the exponential (a) Suppose you are model Y, Ae, BX. Derive the linearized model to which we can find a line of best fit (in the least squares sense). 3 marks (b) The lines of best fit for two repetitions of an experiment are reproduced below: Each data set has an obvious outlier. In each case, explain the effect that removing the outlier from the data set will have on...
8. (16 points) Suppose you use a quadratic curve y = ax? +b to fit the three (x,y) points (1,3), (0,-1), (-1,1). Use matrix method as described in class to find the least squares estimate of the constants a and b in the above equation. In particular, formulate the relevant normal equation, whose solution leads to the least squares estimates of a and b, and hence obtain the least squares estimate of a and b.
Linear Algebra
To fit data to an exponential model like y = AeKt, we first use a logarithm to linearize it: . n y n A k t Since A is a constant, so is ln A, and we can write this generically as ln y = co + cit. The table below shows the years different planes were first produced, along with how many displays (gauges, screens, etc.) were present in the cockpit. Year Introduced, y (Year after 1900)...
please answer a) and b) but ignore the matlab part in
b)
1. The following data represents the bacterial growth in a liquid culture over a number of days x (days) 0 4 8 12 16 20 y (amount=106) 67.38 74.67 82.74 91.69 101.60 112.58 a) Apply linear least-squares regression (by hand) to find the best straight line to fit the data. b) Apply polynomial regression to find the best quadratic polynomial to fit the data. Calcu- late the equations...
This is how you import the Carseats data into Rstudio
software:
library(“ISLR”)
data(“Carseats”)
view(Carseats)
after that, please provide codes for following:
a. Split the data into a training set and a test set. b. Fit a linear model using least squares on the training set to predict Sales using the entire collection of predictors. Report the Cp, BIC, R2, and RSS for this model c. Use the fitted model to predict responses for the test data and report the test...
9) Suppose you are given n points: (x,y)(, y). And we wish to fit a cirele to the data. A general circle, as we all know, is Cr-y+-k. So the question becomes: What are h, k, and r so that the circle becomes the best least squares fit? Show that this problem becomes Th .e. What is a, B and what is M? B, When fitting the cirele to the data points (0,2), (1,2),3,-),(0,-D,6,0) what are the normal equations? GIVE...
67. Recently, the annual number of driver deaths per 100,000 for the selected age groups was as follows: Age Number of Driver Deaths per 100,000 16-19 38 20-24 36 25-34 24 35-54 20 55-74 18 75+ 28 Table 12.19 a For each age group, pick the midpoint of the interval for the x value. (For the 75+ group, use 80) b using ages as the independent variable and "Number of driver deaths per 100.000" as the dependent variable, make a...
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