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9) Suppose you are given n points: (x,y)(, y). And we wish to fit a cirele to the data. A general...
(a) Suppose you are given the following (x, y) data pairs
(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...
3. Normal equations for n points to fit the line y = mx + c: ri 72 yi Problem 1 The data points i...
3. Normal equations for n points to fit the line y = mx + c: ri 72 yi Problem 1 The data points in the table are given. -2.4 | -5.0 20.81.5 0.3 2.5 1.9 6.4 3.2 11.0 3 Total (a) Fit the best line - to the points (b) Fit the best line y- mr + c to the points (c) Plot the data points and the best fit lines in (a) and (b). Which of the lines is...
4. Consider the following data. 16 74 900 29810 (a) Suppose you would like to fit...
4. Consider the following data. 16 74 900 29810 (a) Suppose you would like to fit a model of the form yCes (C and k are constants) to this data. Transform the model in such a way that you can use linear least squares to determine C and k. (b) For this data set, use the following equations to find a best fit line. and (e) Use your calculation from part b) to find the model y - Cek for...
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...
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)...
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...
(a) Suppose you are given the following (x, y) data pairs. x 1 2 6 y...
(a) Suppose you are given the following (x, y) data pairs. x 1 2 6 y 4 3 7 Find the least-squares equation for these data (rounded to three digits after the decimal). ŷ = + x (b) Now suppose you are given these (x, y) data pairs. x 4 3 7 y 1 2 6 Find the least-squares equation for these data (rounded to three digits after the decimal). ŷ = + x (c) In the data for parts...
(a) Suppose you are given the following (x, y) data pairs. x 1 2 5 y...
(a) Suppose you are given the following (x, y) data pairs. x 1 2 5 y 2 1 8 Find the least-squares equation for these data (rounded to three digits after the decimal). ŷ = + x (b) Now suppose you are given these (x, y) data pairs. x 2 1 8 y 1 2 5 Find the least-squares equation for these data (rounded to three digits after the decimal). ŷ = + x (c) In the data for parts (a) and (b), did...
Bonus question 7. Suppose that a scientist has reason to believe that two quantities and y...
Bonus question 7. Suppose that a scientist has reason to believe that two quantities and y are related linearity, that is, y = mc + b, at least approximately, for some values of m and b. The scientist performs an experiment and collects data in the form of points (1,1), (22, y2),..., nyn), and then plots these points. The points don't lie exactly on a straight line, so the scientist wants to find the constants m and b so that...
Consider the following: (a) Suppose you are given the following x, y data pairs. x 2...
Consider the following: (a) Suppose you are given the following x, y data pairs. x 2 1 6 y 6 7 8 Find the least-squares equation for these data. (Use 3 decimal places.) = + x (b) Now suppose you are given these x, y data pairs. x 6 7 8 y 2 1 6 Find the least-squares equation for these data. (Use 3 decimal places.) = + x (c) In the data for parts (a) and (b), did we simply exchange...
3. Normal equations for n points to fit the line y = mx + c: ri 72 yi Problem 1 The data points in the table are given. -2.4 | -5.0 20.81.5 0.3 2.5 1.9 6.4 3.2 11.0 3 Total (a) Fit the best line - to the points (b) Fit the best line y- mr + c to the points (c) Plot the data points and the best fit lines in (a) and (b). Which of the lines is...
4. Consider the following data. 16 74 900 29810 (a) Suppose you would like to fit a model of the form yCes (C and k are constants) to this data. Transform the model in such a way that you can use linear least squares to determine C and k. (b) For this data set, use the following equations to find a best fit line. and (e) Use your calculation from part b) to find the model y - Cek for...
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...
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)...
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...
Bonus question 7. Suppose that a scientist has reason to believe that two quantities and y are related linearity, that is, y = mc + b, at least approximately, for some values of m and b. The scientist performs an experiment and collects data in the form of points (1,1), (22, y2),..., nyn), and then plots these points. The points don't lie exactly on a straight line, so the scientist wants to find the constants m and b so that...
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