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{"ops":[{"insert":"Write a  C++ program:\n"},{"attributes":{"bold":true},"insert":"linear regression least-squares method"},{"insert":"\n"},{"attributes":{"bold":true},"insert":"Purpose:"},{"insert":"\u00a0Fit data using non-linear regression least-squares method for an exponential function.\n"},{"attributes":{"bold":true},"insert":"Discussion:"},{"insert":"\u00a0A hospital administrator wished to develop a regression model for predicting the degree of long-term recovery after discharge from the hospital for severely injured patients. The predictor variable to be utilized is number of days of hospitalization (X), and the response variable is a prognostic index for long- term recovery (Y), with large values of the index reflecting a good prognosis. Data for 15 patients were studied and are presented in a file Related earlier studies reported in the literature found the relationship between the predictor variable and the response variable to be\u00a0"},{"attributes":{"bold":true},"insert":"exponential."},{"insert":"\u00a0Hence, it was decided to investigate the appropriateness of the two-parameter nonlinear exponential regression mode.\n"},{"attributes":{"bold":true},"insert":"data.txt:"},{"insert":"\nDays\u00a0\u00a0Prognostic_index\n2\u00a0\u00a054\n5\u00a0\u00a050\n7\u00a0\u00a045\n10\u00a0\u00a037\n14\u00a0\u00a035\n19\u00a0\u00a025\n26\u00a0\u00a020\n31\u00a0\u00a016\n34\u00a0\u00a018\n38\u00a0\u00a013\n45\u00a0\u00a08\n52\u00a0\u00a011\n53\u00a0\u00a08\n60\u00a0\u00a04\n65\u00a0\u00a06\nFor the data in the file, the function has the form \ud835\udc41 = \ud835\udc4e\ud835\udc52"},{"attributes":{"script":"super"},"insert":"\ud835\udc4f\ud835\udc65"},{"insert":"\u00a0where \ud835\udc4e and \ud835\udc4f are constants that are determined from the fit. Until the user wishes to quit the application should do the following:\nRead data from a file"},{"attributes":{"list":"bullet"},"insert":"\n"},{"insert":"Print the data"},{"attributes":{"list":"bullet"},"insert":"\n"},{"insert":"Print report summary of the data (mean, median, range, mood, and standard Deviation)"},{"attributes":{"list":"bullet"},"insert":"\n"},{"insert":"Do an exponential fit and print the regression equation"},{"attributes":{"list":"bullet"},"insert":"\n"},{"insert":"Compute how accurate your exponential fit (Standard Error)"},{"attributes":{"list":"bullet"},"insert":"\n"},{"insert":"Offer an interpolation\/extrapolation of both the prognostic index."},{"attributes":{"list":"bullet"},"insert":"\n"},{"insert":"The exponential data has to be transformed to have a linear relation. Then find the value of a and b using the equations given in your lecture\u2019s slides.\nOffer the user the option of interpolating \/ extrapolating the data to find what the prognostic index will be in other days.\n\n"},{"attributes":{"italic":true,"bold":true},"insert":"Example Output"},{"insert":"\n\nLEAST_SQUARES LINEAR REGRESSION\nMENU\nExponential Fit"},{"attributes":{"list":"ordered"},"insert":"\n"},{"insert":"Quit"},{"attributes":{"list":"ordered"},"insert":"\n"},{"insert":"1\nPlease enter the name of the file to open: data.txt Days\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Prognostic_index\n2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a054\n5\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a050\n7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a045\n10\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a037\n14\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a035\n19\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a025\n26\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a020\n31\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a016\n34\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a018\n38\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a013\n45\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a08\n52\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a011\n53\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a08\n60\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a04\n65\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a06\nThere are 15 records.\nData summary (Prognostic index):\nMean =??? Median=??? Range=???\nMode=???\nStandard Deviation=???\nLinear Regression Fit: Prognostic_index = ???*exp -???*days Stander Error=???\nMENU\nExtrapolation"},{"attributes":{"list":"ordered"},"insert":"\n"},{"insert":"Main Menu 1"},{"attributes":{"list":"ordered"},"insert":"\n"},{"insert":"Please enter the days to extrapolate to: 33 days = 33\nPrognostic_index = 16.2\nMENU\nExtrapolation"},{"attributes":{"list":"ordered"},"insert":"\n"},{"insert":"Main Menu 1"},{"attributes":{"list":"ordered"},"insert":"\n"},{"insert":"Please enter the days to extrapolate to: 73 days = 73\nPrognostic_index = 3.54\nMENU\nExtrapolation"},{"attributes":{"list":"ordered"},"insert":"\n"},{"insert":"Main Menu 2"},{"attributes":{"list":"ordered"},"insert":"\n"},{"insert":"LEAST_SQUARES LINEAR REGRESSION MENU\nExponential Fit"},{"attributes":{"list":"ordered"},"insert":"\n"},{"insert":"Quit"},{"attributes":{"list":"ordered"},"insert":"\n"},{"insert":"\n"}]}

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