Question

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) Plane Number of Displays, n 35 Douglas DC-3 Lockheed Constellation 35 46 46 59 Boeing 707 77 Aerospatiale Concorde 69 133 Usc the cast-squares method to find the function of the form log n = Co above data c1y that best fits the a) Show the matrix equation for which you are finding an approximate solution as well as the equation you enter in your calculator. On paper, round answers to the nearest hundredth, but use the full accuracy in your calculator. b) Use your results to write the function that is the best fit to the above data. If necessary, round coefficients to three decimal places

Answer 1

Any qquery then comment below.. i willl help you..

log^n = c_0 + c_1 y E = Sigma^4_i = 1 (log n_1 - C_0 - c_1 y_i)^2 partial differential E/partial differential C_0 implies u C_0 + C_1 Sigma y_i = Sigma log(n_i) implies 4 C_0 + 209 C_1 = 7.217168242 partial differential E/partial differential C_1 = 0 implies C_0 Sigma y_i + C_1 Sigma y^2_1 = Sigma y'_1 log (m) implies 209 C_1 + 11583 C_1 = 388.3779578 So, [4 209 209 11583][c_0 c_1] = [7.22 388.38] By solving these, we get C_0 = 0.91492515, C_1 = 0.0170214 C_0 = 0.915, C_1 = 0.017 A = e^C_0 = 2.496588 y = 2.497 e^0.017 t