▸ Question #19: Let X1 be the value of X associated with the point of intersection between the equations: Y=255-(3) X and Y = 13+ ( 3 ) X and let X2 = X1 + 5. What is the difference between the under curve areas of the two equations?
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- Determine the coefficients a, b, c, and d so that the curve will satisfy the stipulated condition. Make the curve y= ax^3+bx^2+cx+d have critical points (1,0) and (-2,27)The regression models that we introduced inSections 2 and 6 are linear in the x’s, but, more important,they are also linear in the β’s. Indeed, they can be usedin some problems where the relationship between the x’sand y is not linear. For instance, when the regression isparabolic and of the form μY|x = β0 + β1x + β2x2 we simply use the regression equation μY|x = β0 + β1x1 +β2x2 with x1 = x and x2 = x2. Use this method to fita parabola to the following data on the drying time ofa varnish and the amount of a certain chemical that hasbeen added:Amount of additive Drying time(grams) (hours)x y1 8.52 8.03 6.04 5.05 6.06 5.57 6.5Also, predict the drying time when 6.5 grams of the chem-ical is added.What is the meaning of the value of parameter bb in this situation?
- In the area of Russia récords were kept on the relationship between the rain Fall in inches and the yield of wheat (bushels per acre ).the data for a 9 year period is as follow. Rain fall x 13.1,11.4,16.0,15.1,21.4,12.9,9.6,18.2,18.6. yield y : 48.5,44.2,56.8,80.4,47.2,29.9,74.0,74.0,76.8 the equation of the line of least squares is given as ^y= -9.12+4.38x. How many bushels of wheat peen acre can be predicted if it’s is expected that there will be 30 inches of rain?Find an equation for the level surface of the function f (x, y) = ln (x² + y²+ z²) that passes through the point (−1,2,1).1. How can you measure the quality of the linear approximation offered by the above model?What is meant by R 2 = 1 and R 2 = 0?