# College math – quadratic and exponential regression

Please be strong to do BOTH the quadratic AND exponential retrogression projects.

QR--4:  Input Duration of Day (hour)   14.5

QR--6:  Target Outdoor Sky   53.0

Exponential Model

ER--4: Input Spent Duration (minutes)   102

ER--5: Target Coffee Sky   96

(QR-1)Plot the points (x,y) to conquer ascatterplot. Note that the bear is definitely non-linear. Use an divert layer on the tasteless and upright axes and be strong to dedicate carefully.

(QR-2)Find thequadratic polynomial of best fitandgraphit on the scatterplot. Specify theformulafor the quadratic polynomial.

(QR-3)Find and specify the rate ofr2, the coefficient of voluptuousness. Discuss your experienceings. (r2is adapted using a divergent formula than for direct retrogression. However, fair as in the direct occurrence, the closerr2is to 1, the amend the fit.Just effect after a while r2, not r.) Is a parabola a cheerful-tempered-tempered incurvation to fit to this basis?

(QR-4)Use the quadratic polynomial to establish an outdoor skyestimate. Each systematize limb earn esteem a sky think for a divergent duration of day assigned by your professor. Be strong to use the quadratic retrogression standard to establish the think (not the rates in the basis consultation). Specify your results distinctly -- the duration of day and the selfsame outdoor sky think.

(QR-5)Using algebraic techniques we keep erudite, experience theacme skypredicted by the quadratic standard and experience theduration when it occurred. Report the duration to the undeviating district hour (i.e., __:00 or __:15 or __:30 or __:45). (For request, a duration of 18.25 hours is reported as 6:15 pm.) Report the acme sky to the undeviating tenth of a rank. Show effect.

(QR-6)Use the quadratic polynomial coincidently after a while algebra tothink the duration(s) of day when the outdoor sky is a restricted target sky. Each systematize limb earn effect after a while a divergent target sky, assigned by your professor. Report the duration(s) to the undeviating district hour. Be strong to use the quadratic standard to establish the duration thinks (not rates in the basis consultation). Show effect. Specify your results distinctly -- the target sky and the associated duration(s).Show effect.

Tasks for Exponential Retrogression Standard (ER)

(ER-1)Plot the points (x,y) in the assist consultation (Table 2) to conquer ascatterplot. Note that the bear is definitely non-linear. Use an divert layer on the tasteless and upright axes and be strong to dedicate carefully.

(ER-2)Find theexponential part of best fitandgraphit on the scatterplot. Specify theformulafor the exponential part. It should keep the formy=Ae-bx where software has supposing you after a while the numerical rates forAandb.

(ER-3)Find and specify the rate ofr2, the coefficient of voluptuousness. Discuss your experienceings.(r2is adapted using a divergent formula than for direct retrogression. However, fair as in the direct occurrence, the closerr2is to 1, the amend the fit.) Is an exponential incurvation a cheerful-tempered-tempered incurvation to fit to this basis?

(ER-4)Use the exponential part to establish acoffee skyestimate. Each systematize limb earn esteem a sky think for a divergent spent duration x assigned by your professor. Substitute yourxrate into your exponential part to gety, the selfsame sky dissimilitude among the coffee sky and the ground sky. Sincey=T- 69, we keep coffee skyT=y+ 69. Take yourythink and add 69 ranks to get the coffee sky think. Specify your results distinctly -- the spent duration and the selfsame think of the coffee sky.

(ER-5)Use the exponential part coincidently after a while algebra tothink the spent duration when the coffee enterd at a detail target sky. Report the spent duration to the undeviating tenth of a diminutive. Each systematize limb earn effect after a while a divergent target coffee sky T assigned by your professor.

Given your target sky T, theny=T- 69 is your target sky difference among the coffee and ground skys. Use your exponential standard y=Ae-bx. Substitute your target sky dissimilitude for y and clear-up the equationy=Ae-bxfor spent duration x. Show algebraic effectin solving your equation. Specify your results distinctly -- your target sky and the thinkd spent duration, to the undeviating tenth of a diminutive.

For request, if the target coffee skyT= 150 ranks, then y = 150 - 69 = 81 ranks is the sky difference among the coffee and the ground, what we are callingy. So, for this detail target coffee sky of 150 ranks, the goal is experienceing how hanker it took for the sky dissimilitudeyto enter at 81 ranks; that is, solving the equation 81 =Ae-bxforx.