Linear
Regression
1 Continuous Dependent Variable with
normal distribution
1 Continuous Independent Variable with
normal distribution
Linear
regression measures the linear relationship between an independent variable, x,
and a dependent variable, y. Building directly from the mathematical equation
for a line, y = mx + b, linear regression tells the researcher the extent to
which x predicts y. When linear regression returns ‘1’, there is a perfect
correlation between x and y, meaning as x increases, y increases
proportionally. When linear regression returns ‘0’, there is no relationship
between x and y. Contrarily, if there is a perfect negative correlation between
x and y, linear regression will return
‘-1’. This
means as x decreases, y decreases proportionally.
There is not
a universally accepted definition of statistical significance in linear
regression. For example, there is no standard stating that if the regression correlation
is > .75, then the results are significant.
Therefore, the researcher must interpret the results and report them as
he/she sees fit. Generally, correlation between .50 and .70 is worth noting as
a trend, and results > .70 represent strong correlation.
In
‘Predicting Text Entry Speed on Mobile Phones’ [11],
Silfverberg et al. develop a model to predict how quickly expert users can
enter text on their cell phones. The team explains creating new cell phone text
entry methods are expensive and are best tested in longitudinal studies. If
developers had a tool to predict how quickly expert users could enter text on
their cell phones, costly prototype development and testing could be minimized.
With this motivation, the researchers develop a model to predict cell phone T9
text entry speed using Fitts’ law of motion.
As part of
the study, subjects perform a series of scripted text entry tasks on a cell
phone. The subjects have 10 seconds to enter a series of carefully chosen key
pairs on the key pad. Some of the key pairs are physically close together on
the cell phone (e.g. 1 and 2), others are physically far apart on the cell
phone key pad (e.g. 3 and *). Subjects enter the key pairs only using only
their thumb. The research team demonstrates a valid application of linear
regression in analyzing the results. The intent is to measure whether there is
correlation between the physical distance between the key pairs entered and the
amount of time it takes to enter the key pairs.
In the
analysis, distance between key pairs serves as the independent variable, and
time to enter text serves as the dependent variable. Linear regression is the
right tool for the experiment because both variables are measured on a
continuous scale, and clearly the research team wants to understand the extent
to which distance between cell phone keys predicts amount of time to enter
text. Using linear regression, the research team found a strong relationship,
.97, correlating the distance between key pairs and time to enter text. The
results are shown in Figure 4 above, along with significant results from a
second experiment the team conducted. The second experiment was identical to
the first, except that in the second test, subjects entered key pairs using
only their index finger.
Values to report:
·
r value
·
intercept
point