JMPIN Instruction for Chapter 18

  1. Example 18.1(pp.684)

Open file XM18-01

Click Analyze and Fit Model, make MARGIN be the Y and Add ROOMS, NEAREST, OFFICE, COLLEGE, INCOME, DISTWIN into the Model Effects Box, then click Run Model.

To see the confidence and prediction intervals, add one more row, then input the value of 3815, 3.4, 476, 24.5, 39, 3.6 for ROOMS, NEAREST, OFFICE, COLLEGE, INCOME, DISTWIN correspondingly. Repeat step 2 above, click on the red triangle in front of Response MARGIN, select Save Columns and pick Mean Confidence Interval and Indiv Confidence Interval (prediction interval), you will have 95% confidence interval as (32.97,41.21) and prediction interval as (25.40, 48.79).

Response MARGIN

Whole Model

Actual by Predicted Plot

ROOMS

Leverage Plot

NEAREST

Leverage Plot

OFFICE

Leverage Plot

COLLEGE

Leverage Plot

INCOME

Leverage Plot

DISTTWN

Leverage Plot

Whole Model

Summary of Fit

RSquare / 0.525062
RSquare Adj / 0.49442
Root Mean Square Error / 5.512084
Mean of Response / 45.739
Observations (or Sum Wgts) / 100

Analysis of Variance

Source / DF / Sum of Squares / Mean Square / F Ratio
Model / 6 / 3123.8320 / 520.639 / 17.1358
Error / 93 / 2825.6259 / 30.383 / Prob > F
C. Total / 99 / 5949.4579 / <.0001

Parameter Estimates

Term / Estimate / Std Error / t Ratio / Prob>|t|
Intercept / 72.454611 / 7.893104 / 9.18 / <.0001
ROOMS / -0.007618 / 0.001255 / -6.07 / <.0001
NEAREST / -1.646237 / 0.632837 / -2.60 / 0.0108
OFFICE / 0.0197655 / 0.00341 / 5.80 / <.0001
COLLEGE / 0.2117829 / 0.133428 / 1.59 / 0.1159
INCOME / -0.413122 / 0.139552 / -2.96 / 0.0039
DISTTWN / 0.2252581 / 0.178709 / 1.26 / 0.2107
  1. Example 18.2(pp700)

Open file XM18-02

Click Analyze and Fit Models; make Price be Y and Add Bedrooms and H Size and Lot Size into the box of model effects, then click Run Model.

Whole Model

Actual by Predicted Plot

Bedrooms

Leverage Plot

H Size

Leverage Plot

Lot Size

Leverage Plot

Response Price

Whole Model

Summary of Fit

RSquare / 0.559998
RSquare Adj / 0.546248
Root Mean Square Error / 25022.71
Mean of Response / 154066
Observations (or Sum Wgts) / 100

Analysis of Variance

Source / DF / Sum of Squares / Mean Square / F Ratio
Model / 3 / 7.65017e10 / 2.5501e10 / 40.7269
Error / 96 / 6.0109e+10 / 626135896 / Prob > F
C. Total / 99 / 1.36611e11 / <.0001

Parameter Estimates

Term / Estimate / Std Error / t Ratio / Prob>|t|
Intercept / 37717.595 / 14176.74 / 2.66 / 0.0091
Bedrooms / 2306.0808 / 6994.192 / 0.33 / 0.7423
H Size / 74.296806 / 52.97858 / 1.40 / 0.1640
Lot Size / -4.363783 / 17.024 / -0.26 / 0.7982
  1. Example 18.3(pp705)

Open file XM18-03

Click Analyze and Fit Y by X; make Mark by Y and Time be X, then click OK.

Click Bivariate Fit of Mark by Time and fit line.

To check for the normality of residual, first click on the red triangle in front of Linear Fit and select Save Residuals, then go back to the original data table and you will find there is one more column named Residuals Mark, Click Analyze and Distribution, then put in Residuals Mark as Y, click OK, it appears the histogram of the residuals, click on the red triangle in front of Residuals Mark and select Normal Quantile Plot.

Note: to change Mark to log (Mark), click Bivariate Fit of Mark by Time and Fit Special, then select Y Transformation: Natural Logarithm, click OK.

Note: to change Mark to 1/Mark, click Bivariate Fit of Mark by Time and Fit Special, then select Y Transformation: Reciprocal, click OK.

Bivariate Fit of Mark By Time

Linear Fit

Mark = -2.2 + 0.55 Time

Summary of Fit

Rsquare / 0.743974
RSquare Adj / 0.741362
Root Mean Square Error / 2.304609
Mean of Response / 25.3
Observations (or Sum Wgts) / 100

Analysis of Variance

Source / DF / Sum of Squares / Mean Square / F Ratio
Model / 1 / 1512.5000 / 1512.50 / 284.7743
Error / 98 / 520.5000 / 5.31 / Prob > F
C. Total / 99 / 2033.0000 / <.0001

Parameter Estimates

Term / Estimate / Std Error / t Ratio / Prob>|t|
Intercept / -2.2 / 1.64582 / -1.34 / 0.1844
Time / 0.55 / 0.032592 / 16.88 / <.0001

Distributions

Residuals Mark

Quantiles

100.0% / maximum / 8.2000
99.5% / 8.2000
97.5% / 6.1500
90.0% / 2.9250
75.0% / quartile / 1.4500
50.0% / median / -0.0500
25.0% / quartile / -1.5500
10.0% / -2.7750
2.5% / -4.1688
0.5% / -5.8000
0.0% / minimum / -5.8000

Moments

Mean / 7.105e-16
Std Dev / 2.2929404
Std Err Mean / 0.229294
upper 95% Mean / 0.4549718
lower 95% Mean / -0.454972
N / 100

Transformed Fit Log

Log(Mark) = 2.1295821 + 0.0217159 Time

Summary of Fit

RSquare / 0.771412
RSquare Adj / 0.769079
Root Mean Square Error / 0.084437
Mean of Response / 3.215377
Observations (or Sum Wgts) / 100

Analysis of Variance

Source / DF / Sum of Squares / Mean Square / F Ratio
Model / 1 / 2.3579010 / 2.35790 / 330.7181
Error / 98 / 0.6987048 / 0.00713 / Prob > F
C. Total / 99 / 3.0566058 / <.0001

Parameter Estimates

Term / Estimate / Std Error / t Ratio / Prob>|t|
Intercept / 2.1295821 / 0.0603 / 35.32 / <.0001
Time / 0.0217159 / 0.001194 / 18.19 / <.0001

Transformed Fit Recip

Recip(Mark) = 0.0845743 - 0.0008765 Time

Summary of Fit

RSquare / 0.777884
RSquare Adj / 0.775617
Root Mean Square Error / 0.003345
Mean of Response / 0.040751
Observations (or Sum Wgts) / 100

Analysis of Variance

Source / DF / Sum of Squares / Mean Square / F Ratio
Model / 1 / 0.00384099 / 0.003841 / 343.2104
Error / 98 / 0.00109675 / 0.000011 / Prob > F
C. Total / 99 / 0.00493774 / <.0001

Parameter Estimates

Term / Estimate / Std Error / t Ratio / Prob>|t|
Intercept / 0.0845743 / 0.002389 / 35.40 / <.0001
Time / -0.000876 / 0.000047 / -18.53 / <.0001
  1. Example 18.4(pp717)

Open file XM18-04

Click Analyze and Fit Models; make Tickets be Y and Add Snowfall and Temperature into the box of model effects, then click Run Model.

Click Response Tickets, Row Diagnostics and Durbin Watson Test.

Response Tickets

Whole Model

Actual by Predicted Plot

Snowfall

Leverage Plot

Temperature

Leverage Plot

Response Tickets

Whole Model

Summary of Fit

RSquare / 0.12003
RSquare Adj / 0.016504
Root Mean Square Error / 1711.676
Mean of Response / 9315.3
Observations (or Sum Wgts) / 20

Analysis of Variance

Source / DF / Sum of Squares / Mean Square / F Ratio
Model / 2 / 6793798 / 3396899 / 1.1594
Error / 17 / 49807214 / 2929836 / Prob > F
C. Total / 19 / 56601012 / 0.3373

Parameter Estimates

Term / Estimate / Std Error / t Ratio / Prob>|t|
Intercept / 8308.0114 / 903.7285 / 9.19 / <.0001
Snowfall / 74.593249 / 51.57483 / 1.45 / 0.1663
Temperature / -8.753738 / 19.70436 / -0.44 / 0.6625

Effect Tests

Source / Nparm / DF / Sum of Squares / F Ratio / Prob > F
Snowfall / 1 / 1 / 6128677.7 / 2.0918 / 0.1663
Temperature / 1 / 1 / 578236.9 / 0.1974 / 0.6625

Durbin-Watson

Durbin-Watson / Number of Obs. / AutoCorrelation
0.5931403 / 20 / 0.5914

Add new column and fill in the corresponding cell with 1, 2, …, 20. And change the name of the column to “Years”. Then Click Analyze and Fit Models; make Tickets be Y and Add Snowfall, Temperature and Years into the box of model effects, then click Run Model.

Response Tickets

Whole Model

Actual by Predicted Plot

Summary of Fit

RSquare / 0.74098
RSquare Adj / 0.692414
Root Mean Square Error / 957.2354
Mean of Response / 9315.3
Observations (or Sum Wgts) / 20

Analysis of Variance

Source / DF / Sum of Squares / Mean Square / F Ratio
Model / 3 / 41940217 / 13980072 / 15.2571
Error / 16 / 14660795 / 916299.68 / Prob > F
C. Total / 19 / 56601012 / <.0001

Parameter Estimates

Term / Estimate / Std Error / t Ratio / Prob>|t|
Intercept / 5965.5876 / 631.2518 / 9.45 / <.0001
Snowfall / 70.183059 / 28.85142 / 2.43 / 0.0271
Temperature / -9.232802 / 11.01971 / -0.84 / 0.4145
Years / 229.96997 / 37.13209 / 6.19 / <.0001

Effect Tests

Source / Nparm / DF / Sum of Squares / F Ratio / Prob > F
Snowfall / 1 / 1 / 5422102 / 5.9174 / 0.0271
Temperature / 1 / 1 / 643227 / 0.7020 / 0.4145
Years / 1 / 1 / 35146419 / 38.3569 / <.0001

Residual by Predicted Plot

Snowfall

Leverage Plot

Temperature

Leverage Plot

Years

Leverage Plot