Prof.Porter / Mercer CountyCollege / Fall2017 / REGRESSION PROJECT WORK SHEET / Part 2
1. Roughlyplot dataandregression. Label Axis.
Find the averagerateof change between the first and last x-values usingregression
2. Roughlysplit the graph into two regions and performdifferentregressions on eachside.Plot dataandregressions. Label Axis.

3.Roughlysplit the graph into two regions and performdifferentregressions on eachside.Plot dataandregressions. Label Axis.

leftregression split at aY1=vars 5: >1: RegEq /(x≤a)
rightregression
Y2=vars 5: >1: RegEq /(x≥a) / LeftRegressionused:
RightRegressionused:
Find Y1(-9999)
Y2(9999) / limr(x)
x
limr(x)
x

4.For acontinuousregression: Given ɛ =small number Find δ0 that satisfiesRoughlyadjust the regressions so the graph is continuous.

Plot dataandgraph the regressions. Label Axis.

BONUS

Y1(x)=regression(y2=splitregression)Y3=L- ɛ
Y4=L+ ɛ
Calc5:intersect y1andy3 =x1Calc5:intersect y1(2)andy4 =x2δ =maximum(|a-x1|,|a- x2|) / limr(x)=L
xa
Givenɛ =
Find δ =
Pick xvalues in order

Find the averagerateof change between the exterior x-values around x =ausingregression

{Y1(x1)-Y1(x6)}/{x1–x6}= msec / AverageRate ofChange

Find the averagerateof change between an interior x-values around x=ausingregression

{Y1(x2)-Y1(x5)}/{x2–x5}= msec / AverageRate ofChange

Find the averagerateof change between themoreinterior x-values around x=ausingregression

{Y1(x3)-Y1(x4)}/{x3–x4}= msec / AverageRate ofChange

Find theinstnataneousrate of changeat x=a

nderiv(y1,x,a)
or calc 6:dydx and x =a / InstantRate ofChange

6. Find the derivativesofdifferentregressions using rules at x=x1

LinearRegressiony1=ax+b / y’=a / y’(x1) =
Quadratic Regressiony2=ax2+bx+c / y’=2ax+b / y’(x1) =
Cubic Regressiony3=ax3+bx2+cx+d / y’=3ax2+2bx+c / y’(x1) =
QuarticRegressiony4=ax4+bx3+cx2+dx+e / y’=4ax3+3bx2+2cx+d / y’(x1) =

Choosearegression,evaluateitatx1: y(x1)=

Accordingtothe

weexpectytobey(x1)= ofy'(x1)=

regression,atx1=

withagrowthrate

Exponentialy6=a*b^x / y’=a*b^x*ln(b) / y’(x1) =
LnRegressiony7=alnx+b / y’=a/x / y’(x1) =

Choosearegression,evaluateitatx1: y(x1)=

Accordingtothe

weexpectytobey(x1)= ofy'(x1)=

regression,atx1=

withagrowthrate

8.Find thesecondderivativesofdifferentregressionsusingrulesatx=x1

LinearRegressiony1=ax+b / y’’= 0 / y’’(x1) =
Quadratic Regressiony2=ax2+bx+c / y’’= 2a / y’’(x1) =
Cubic Regressiony3=ax3+bx2+cx+d / y’’= 6ax+2b / y’’(x1) =
QuarticRegressiony4=ax4+bx3+cx2+dx+e / y’’=12ax2+6bx+2c / y’’(x1) =

Choosearegression,evaluateitatx1: y(x1)=

Accordingtothe

weexpectytobey(x1)=

regression,atx1=

withagrowthrate

ofy'(x1)=

anditis

9.Makea transformation ofyour x-valuesandyoury-values

New x-values (units) / Old x-values(units)
Old x-values(units) / Oldy-values(units)
Oldy-values(units) / Newy-values(units)

10.Find the derivativesof sine regression usingrulesat x=x1

Sine Regressiony2=asin(bx+c)+d / y’=acos(bx+c)*b / y’(x1) =

Find the second derivatives of sine regression usingrulesat x=x1

Sine Regressiony2=asin(bx+c)+d / y’’= -asin(bx+c)*b^2 / y’’(x1) =

Accordingtothesine regressionwithaperiodof

,at

x1=weexpectytobey(x1)=

withagrowthrateof

y'(x1)=

anditis

11.Usethe mean value theorem on thetwo end points OFaregressionand identifyapoint on thegraphwith a similarslope?
12. Was the zerofoundbyusingNewton’s Method for byusingx=0 or x=1 as an initialguess?Y1=cubicregression
0 sto x
x-y1/nderv(y1,x,x)stox
iterationiterationiteration
zero:
13.

X:
Y’
Increasingor Deceasing
Y’’
Concavity?Up or Down

15.

Findy=0to identifycritical valuesa1,a2

Findy’’(a1)andy”(a2) todetermine max/min

Y’’atcriticalPoints
Maxor Min

16. Findy’’=0 to identifyinflection points Did the student takethesecond derivative and identifyconcavityforthe zero ofthecubicregression? Y’’=0 at –b/(6a):