Use five decimal places Fit the following data by the equation y=(a*x)/(b+x) using the Least squares method x 2 4 10 13 y 15 32 40 24
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Use five decimal places
Fit the following data by the equation y=(a*x)/(b+x) using the Least squares method
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- Fit a curve of the form g(x) = A10Bx to the dataset using the Least Squares Method. Calculate the corrected values and the total squared error.Calculate Pearson’s coefficient of skewness. Hence, describe the shape of thedistribution of the waiting time for counter A and B.Assume that the table below displays the number of freight tonnes carried (in millions) in Australia between 1990 and 2015.Year199019952000200520102015Number of freight tonnes (millions)6684104126160186a) Draw a scatter diagram of the data.b) Find the least squares regression line of number of freight tonnes (in millions) carried on a year. (Note: Use only the last two digits of the year).c) Draw the line in (b) on the scatter diagram in (a). Comment on whether you feel the line is a good fit of the data.d) Use the line in (b) to predict the number of freight tonnes that might be carried in Australia in both 2020 and 2025.e) Do you think your predictions in (d) will be relatively accurate? Why or why not?
- A medical experiment on tumor growth gives the following data table. X: 65, 70, 86, 100, 222. Y: 33, 35, 45, 52, 70. The least squares regression line was found. Using technology, it is determined that the total sum of squares (SST) was 898 and the sum of squares of regression (SSR) was 806.2. Calculate R2, rounded to three decimal placesDisk drives once more Here are the residuals for aregression of Price on Capacity for the hard drives ofExercise 18.a) Which residual contributes the most to the sum that isminimized by the Least Squares criterion?b) Two of the residuals are negative. What does that meanabout those drives? Be specific and use the correct units.Design a 3rd order Least-squares function approximation to interpolate between the mid between (2n and 3") for a dataset as chosen by you. Compute the LS model error.
- Sales of a particular product for the years 2017 through 2020 have been 47,505, 53,010, 49,385 and 81,933 respectively. What sales would you forecast for 2021 using the simple regression (least squares) method?The data in the table represent the weights of various domestic cars and their miles per gallon in the city for the 2008 model year. For these data, the least-squares regression line is y=−0.006x+42.541. A twelfth car weighs 3,425pounds and gets 12 miles per gallon. (a) Compute the coefficient of determination of the expanded data set. What effect does the addition of the twelfth car to the data set have on R2? (b) Is the point corresponding to the twelfth car influential? Is it an outlier? Car Weight_(pounds),_x Miles_per_Gallon,_y1 3767 212 3989 193 3534 204 3175 225 2581 276 3736 207 2606…Table gives life expectancies for people born in the United States in the given years. (a) Determine the least squares approximating line for these data and use it to predict the life expectancy of someone born in 2000. (b) How good is this model? Explain.
- A regression analysis between weight (y in pounds) and height (x in inches) resulted in following least squares line: y^= 120+5x. this implies that if the height is increased by 1 inch, the weight is expected ?An owner of a home in the Midwest installed solar panels to reduce heating costs. After installing the solar panels, he measured the amount of natural gas used y (in cubic feet) to heat the home and outside temperature x (in degree-days, where a day's degree-days are the number of degrees its average temperature falls below 65° F) over a 23-month period. He then computed the least-squares regression line for predicting y from x and found it to be ŷ = 85 + 16x. The software used to compute the least-squares regression line for the equation above says that r2 = 0.98. This suggests which of the following? 1. Gas used increases by square root of 0.98 = 0.99 cubic feet for each additional degree-day? 2. Although degree-days and gas used are correlated, degree-days do not predict gas used very accurately. 3. Prediction of gas used from degree-days will be quite accurate.A chemical engineer discovered that by adding different amounts of an additive to gasoline, he could reduce the amount of nitrous oxides (NOx) from a car engine. A specified amount was added to one gallon of gasoline and the total amount of NOx in the exhaust was collected. Assume, in suitable units, that the data is: amount of additive 1 2 3 4 5 Nox 19 17 14 13 12 a) Obtain the least squares fit, of a straight line, for the amount of NOx b) Test whether or not the slope is β = 0. Consider a significance level of 0.01. c) Provide a 99% confidence interval for the mean value of NOx when the amount of additive is 9.
