Supplementary Exercise 2.59 of IPS7e
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Data on reaction time (with computer mouse) and distance on computer screen for 40
trials carried out by one subject, 20 with each hand. The reaction time is a response
variable whereas the distances between successive points on the screen are controlled
in the trial (determined by the software). The hand used is an explanatory variable.


(a) Minitab commands for requested plot:

MTB > WOpen "H:\VHM\VHM801\Datasets\Minitab\Chapter 2\ex02_059.mtw".
Retrieving worksheet from file: 'H:\VHM\VHM801\Datasets\Minitab\Chapter
2\ex02_059.mtw'
Worksheet was saved on 07/11/2014

MTB > Plot 'time'*'dist';
SUBC>   Symbol 'hand'.
Scatterplot of time vs dist 

(b) Interpretation of plot:

- The right-hand points lie below the left-hand points. This means that
the right-hand times are shorter, so the subject is right-handed.
- The left-hand points show a wide scatter with perhaps a slight tendency
towards larger reaction times with larger distances.
- The right-hand points are squeezed together at the bottom of the plot,
so it is difficult to see any patterns; however, there does not seem to
be any clear dependence of reaction times on distance.

(c) Minitab command for plot with two regressions (within same worksheet):

MTB > Plot 'time'*'dist';
SUBC>   Symbol 'hand';
SUBC>   Regress 'hand'.
Scatterplot of time vs dist 

It is seen that the slopes are quite different, steeper for the left
hand. The two regression lines can be read of the plot by moving the
pointer to each of the lines. Realistically it is more practical to do
separate analyses for the left-hand and right-hand data, and for this we
will split the Minitab worksheet by the variable hand.

MTB > Split;
SUBC>   NoMatrices;
SUBC>   NoConstants;
SUBC>   By 'hand'.
Results for hand = left 
Results for hand = right 

Results for: ex02_059.mtw(hand = right)
MTB > Fitline 'time' 'dist';
SUBC>   GFourpack;
SUBC>   RType 1;
SUBC>   Confidence 95.0.
Regression Analysis: time versus dist 

The regression equation is
time = 99.36 + 0.02831 dist

S = 8.06850   R-Sq = 9.3%   R-Sq(adj) = 4.2%

Analysis of Variance

Source      DF       SS       MS     F      P
Regression   1   119.94  119.939  1.84  0.191
Error       18  1171.81   65.101
Total       19  1291.75
 
Fitted Line: time versus dist 

Results for: ex02_059.mtw(hand = left)
MTB > Fitline 'time' 'dist';
SUBC>   GFourpack;
SUBC>   RType 1;
SUBC>   Confidence 95.0.
Regression Analysis: time versus dist 

The regression equation is
time = 171.5 + 0.2619 dist

S = 71.1125   R-Sq = 10.1%   R-Sq(adj) = 5.1%

Analysis of Variance

Source      DF      SS       MS     F      P
Regression   1   10266  10266.1  2.03  0.171
Error       18   91026   5057.0
Total       19  101292
 
Fitted Line: time versus dist 

Comments:
---------
The statistical models (for left-hand and right-hand data) are  linear
regression models:
  time_i = beta0 + beta1 * dist_i + eps_i
where the errors (eps_i) are i.i.d. from N(0,sigma), and the model
parameters (beta0, beta1, sigma) are different for left and right hands.

The fitted line plots for the two subsets look quite similar when viewed
on their own scale: the points are scattered widely around a line with a
slightly increasing slope. None of the separate regressions correspond
to a significant association between distance and time (P=0.17 and
P=0.19).

The following table summarizes the results:

hand      intercept  slope    stand.dev.   R^2
left      171.5      0.262    71.1         10.1%
right     99.4       0.0283   8.07         9.3%

The estimated line for the left hand is steeper and the points have a
much larger spread about the line, both by a factor of about 10 relative to 
the right hand. The intercept for the left-hand line is about twice that of
the right-hand line, corresponding to the reaction time for a point that 
requires no movement of the mouse. The two regressions have similar strength 
of association when assessed by the P-value for the test for no association
(this comparison makes sense because the two subsets are of the same size)
and also by the R^2, the proportion of variance explained (the numerical
measure requested). To describe the R^2 as a measure of the "success of
the regression" is in my view poor terminology. Another potential
measure of the predictive ability of the regression is the spread about
the regression line, but this measure is difficult to compare between the two
datasets because the left-hand values by themselves are far more variable.

(d) The 4-in-1 panels of residual plots produced in (c) included in the
lower right corner a plot of the residuals against observation order. No
obvious increasing or decreasing trends are seen in these plots, neither
for the left nor for the right hand. We therefore conclude that none of 
the suggested systematic trends are visible in the data.