Non-Linear regression

What is the best function type to model this data set?

• Linear function.

• Exponential function.

• Quadratic function.

• Cubic function.

Answer explanation

Linear function is of the form y=a+bx. Exponential function is of the form y = Ae^kx. A quadratic function is of the form y =ax²+bx+c and this is a parabola that has an axis of symmetry passing through its vertex. This is the shape best to model this data. A cubic has the form y=ax³+bx²+cx+d.

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.LE.A.2

CCSS.HSF.IF.C.7

CCSS.HSF.LE.A.1

Use regression in your GDC to find a model for this set of data. Report values accurate to 3 significant figures.

Answer explanation

Enter x into L1 and y into L2 in GDC. When finished, press [2nd][Mode] to quit. Press [Stat]->CALC->5:QuadReg [Enter]. You can store the regression in Y1 as Var.

Tags

CCSS.HSS.ID.B.6

CCSS.HSA.CED.A.2

Use regression in your GDC to find a model for this set of data. Find the coefficient of determination of your model accurate to 3 significant figures.

Answer explanation

The coefficient of determination is R². Press [Mode] and make sure your diagnotistics is "ON" as shown here.

Tags

CCSS.HSS.ID.B.6

CCSS.HSS.ID.C.8

R² gives the porportion of variability in y accounted for by the chosen model, i.e. y = f(x).

• True.

• False.

Tags

CCSS.HSF.LE.B.5

Let the R² of a quadratic model is 0.89 then ___ of the variability in y is explained by the quadratic model.

• 11%

• 89%

• 0.89%

• 0.11%

The formula for the coefficient of determination R² = 1 - SS_res/SS_tot. The sum of square residuals is SS_res and this is usually taken as a measure of fit for a model by itself. Thus, R² can be seen as a variation of SS_res.

• True

• False

The formula for the coefficient of determination R² = 1 - SS_res/SS_tot. The total sum of squares is SS_tot. SS_tot is just n(variance of y)

• True

• False

Tags

CCSS.HSS.ID.C.7

Use GDC to find an appropriate regression model for this set of data accurate to 3 significant figures.

Tags

CCSS.HSF.LE.A.2

• SSres

• SStot

• variance of y

• n(variance of y)

Let the model for this data be y = 2^x. Find the SS_res accurate to 3 significant figures.

Answer explanation

L3=2^x which is the given model. The SSres is obtained from [2nd][0] for Catalogue and [Alpha][LN] to jump to S. Move to sum( . Enter sum((L3-L2)²) to obtain 0.305.

Tags

CCSS.HSF.LE.A.2

CCSS.HSF.LE.A.1

CCSS.HSA.SSE.A.1