Question

x y

9 10

32 20

18 21

15 16

26 22

a)Develop an estimated regression equation for the data of the form ŷ = b0+b1x. Plot the standardized residuals againstŷand the normal probability plot. Do the plots support the assumptions about ε? Explain.

b)Develop an estimated regression equation for the data of the form ŷ =b0+b1x+b2x2. Plot the standardized residuals againstŷand the normal probability plot. Do the plots support the assumptions about ε? Explain.

c)Use the estimated regression equation developed in part (b) and predict the value of y when x=20.

provide answer with minitab please

Answer 1

a)

MTB > Regress 'Y' 1 'X';
SUBC> GFits;
SUBC> RType 1;
SUBC> Constant;
SUBC> Brief 2.

Regression Analysis: Y versus X

The regression equation is
Y = 9.32 + 0.424 X

Predictor Coef SE Coef T P
Constant 9.315 4.196 2.22 0.113
X 0.4242 0.1944 2.18 0.117

S = 3.531 R-Sq = 61.4% R-Sq(adj) = 48.5%

Analysis of Variance

Source DF SS MS F P
Regression 1 59.39 59.39 4.76 0.117
Residual Error 3 37.41 12.47
Total 4 96.80

Residuals vs Fits for Y

MTB > Regress 'Y' 1 'X';
SUBC> GFits;
SUBC> RType 1;
SUBC> Constant;
SUBC> Brief 2.

Regression Analysis: Y versus X

The regression equation is
Y = 9.32 + 0.424 X

Predictor Coef SE Coef T P
Constant 9.315 4.196 2.22 0.113
X 0.4242 0.1944 2.18 0.117

S = 3.531 R-Sq = 61.4% R-Sq(adj) = 48.5%

Analysis of Variance

Source DF SS MS F P
Regression 1 59.39 59.39 4.76 0.117
Residual Error 3 37.41 12.47
Total 4 96.80

Residuals vs Fits for Y

MTB > %NormPlot 'RESI2'.
Executing from file: C:\Program Files (x86)\MTBWIN\MACROS\NormPlot.MAC
Macro is running ... please wait

Normal Prob Plot: RESI2

From the plot we can say that follows normal distribution.

b)

MTB > let c3=c1*c1
MTB > Regress 'Y' 2 'X' 'X2';
SUBC> GFits;
SUBC> RType 1;
SUBC> Constant;
SUBC> Brief 2.

Regression Analysis: Y versus X, X2

The regression equation is
Y = - 8.10 + 2.41 X - 0.0480 X2

Predictor Coef SE Coef T P
Constant -8.101 4.104 -1.97 0.187
X 2.4127 0.4409 5.47 0.032
X2 -0.04797 0.01050 -4.57 0.045

S = 1.279 R-Sq = 96.6% R-Sq(adj) = 93.2%

Analysis of Variance

Source DF SS MS F P
Regression 2 93.529 46.765 28.60 0.034
Residual Error 2 3.271 1.635
Total 4 96.800

Source DF Seq SS
X 1 59.394
X2 1 34.135

Residuals vs Fits for Y

MTB > Name c4 = 'RESI1'
MTB > Regress 'Y' 2 'X' 'X2';
SUBC> Residuals 'RESI1';
SUBC> GFits;
SUBC> RType 1;
SUBC> Constant;
SUBC> Brief 2.

Regression Analysis: Y versus X, X2

When x=20

MTB > let k1=-8.10+2.41*20-0.0480*(20*20)
MTB > print k1

Data Display

K1 20.9000