College math – quadratic and exponential regression


 

Please be confident to do BOTH the quadratic AND exponential retreat projects.

 

 

 

Quadratic Model

 

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

 

 

 

QR--6:  Target Outdoor Latitude   53.0

 

 

 

 

 

Exponential Model

 

 

 

ER--4: Input Gone-by Term (minutes)   102

 

 

 

ER--5: Target Coffee Latitude   96

 

 

 

Tasks for Quadratic Retreat Design (QR)

 

(QR-1)Plot the points (x,y) to get ascatterplot. Note that the bear is definitely non-linear. Use an alienate lamina on the tame and upright axes and be confident to write carefully.

 

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

 

(QR-3)Find and recite the esteem ofr2, the coefficient of gratification. Discuss your discoverings. (r2is adapted using a unanalogous formula than for rectirectirectistraight retreat. However, sound as in the rectirectirectistraight request, the closerr2is to 1, the amend the fit.Just performance delay r2, not r.) Is a parabola a amiable flexion to fit to this postulates?

 

(QR-4)Use the quadratic polynomial to effect an outdoor latitudeestimate. Each collocate portion accomplish calculate a latitude like for a unanalogous term of day assigned by your tutor. Be confident to use the quadratic retreat design to effect the like (not the esteems in the postulates board). Recite your results perspicuously -- the term of day and the selfsame outdoor latitude like.

 

(QR-5)Using algebraic techniques we feel well-informed, discover thecompletion latitudepredicted by the quadratic design and discover theterm when it occurred. Report the term to the direct locality hour (i.e., __:00 or __:15 or __:30 or __:45). (For request, a term of 18.25 hours is reported as 6:15 pm.) Report the completion latitude to the direct tenth of a measure. Show performance.

 

(QR-6)Use the quadratic polynomial contemporaneously delay algebra tolike the term(s) of day when the outdoor latitude is a feature target latitude. Each collocate portion accomplish performance delay a unanalogous target latitude, assigned by your tutor. Report the term(s) to the direct locality hour. Be confident to use the quadratic design to effect the term likes (not esteems in the postulates board). Show performance. Recite your results perspicuously -- the target latitude and the associated term(s).Show performance.

 

 

 

Tasks for Exponential Retreat Design (ER)

 

(ER-1)Plot the points (x,y) in the remedy board (Table 2) to get ascatterplot. Note that the bear is definitely non-linear. Use an alienate lamina on the tame and upright axes and be confident to write carefully.

 

(ER-2)Find theexponential character of best fitandgraphit on the scatterplot. Recite theformulafor the exponential character. It should feel the formy=Ae-bx where software has supposing you delay the numerical esteems forAandb.

 

(ER-3)Find and recite the esteem ofr2, the coefficient of gratification. Discuss your discoverings.(r2is adapted using a unanalogous formula than for rectirectirectistraight retreat. However, sound as in the rectirectirectistraight request, the closerr2is to 1, the amend the fit.) Is an exponential flexion a amiable flexion to fit to this postulates?

 

(ER-4)Use the exponential character to effect acoffee latitudeestimate. Each collocate portion accomplish calculate a latitude like for a unanalogous gone-by term x assigned by your tutor. Substitute yourxesteem into your exponential character to gety, the selfsame latitude variety among the coffee latitude and the ground latitude. Sincey=T- 69, we feel coffee latitudeT=y+ 69. Take yourylike and add 69 measures to get the coffee latitude like. Recite your results perspicuously -- the gone-by term and the selfsame like of the coffee latitude.

 

(ER-5)Use the exponential character contemporaneously delay algebra tolike the gone-by term when the coffee landd at a feature target latitude. Report the gone-by term to the direct tenth of a microscopic. Each collocate portion accomplish performance delay a unanalogous target coffee latitude T assigned by your tutor.

 

Given your target latitude T, theny=T- 69 is your target latitude difference among the coffee and ground latitudes. Use your exponential design y=Ae-bx. Substitute your target latitude variety for y and unfold the equationy=Ae-bxfor gone-by term x. Show algebraic performancein solving your equation. Recite your results perspicuously -- your target latitude and the liked gone-by term, to the direct tenth of a microscopic.

 

For request, if the target coffee latitudeT= 150 measures, then y = 150 - 69 = 81 measures is the latitude difference among the coffee and the ground, what we are callingy. So, for this feature target coffee latitude of 150 measures, the motive is discovering how covet it took for the latitude varietyyto land at 81 measures; that is, solving the equation 81 =Ae-bxforx.