# College math – quadratic and exponential regression

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

**Quadratic Model**

**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

**Tasks for Quadratic Retrogression Standard (QR)**

**(QR-1)**Plot the points (*x*,*y*) to conquer a**scatterplot**. 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 the**quadratic polynomial of best fit**and**graph**it on the scatterplot. Specify the**formula**for the quadratic polynomial.

**(QR-3)**Find and specify the rate of**r**** ^{2}**, the coefficient of voluptuousness. Discuss your experienceings. (

*r*

^{2}is adapted using a divergent formula than for direct retrogression. However, fair as in the direct occurrence, the closer

*r*

^{2}is to 1, the amend the fit.Just effect after a while

**r****, not**

^{2}*r*.) Is a parabola a cheerful-tempered-tempered incurvation to fit to this basis?

**(QR-4)**Use the quadratic polynomial to establish an outdoor sky**estimate**. 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 the**acme sky****predicted by the quadratic standard **and experience the**duration 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 to**think 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 a**scatterplot**. 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 the**exponential part of best fit**and**graph**it on the scatterplot. Specify the**formula**for the exponential part. It should keep the form*y*=*A**e*^{-bx} where software has supposing you after a while the numerical rates for*A*and*b*.

**(ER-3)**Find and specify the rate of**r**** ^{2}**, the coefficient of voluptuousness. Discuss your experienceings.(

*r*

^{2}is adapted using a divergent formula than for direct retrogression. However, fair as in the direct occurrence, the closer

*r*

^{2}is 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 a**coffee sky****estimate**. Each systematize limb earn esteem a sky think for a divergent spent duration *x* assigned by your professor. Substitute your*x*rate into your exponential part to get*y*, the selfsame sky dissimilitude among the coffee sky and the ground sky. Since*y*=*T*- 69, we keep coffee sky*T*=*y*+ 69. Take your*y*think 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 to**think 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*, then*y*=*T*- 69 is your target sky *difference* among the coffee and ground skys. Use your exponential standard *y*=*A**e*^{-bx}. Substitute your target sky dissimilitude for *y* and clear-up the equation*y*=*A**e*^{-bx}for spent duration *x. ***Show algebraic effect**in 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 sky*T*= 150 ranks, then *y* = 150 - 69 = 81 ranks is the sky *difference* among the coffee and the ground, what we are calling*y*. So, for this detail target coffee sky of 150 ranks, the goal is experienceing how hanker it took for the sky dissimilitude*y*to enter at 81 ranks; that is, solving the equation 81 =*A**e*^{-bx}for*x*.