Math 338
Lab Activity #3
Daniel Jordan
Application 1:
a. Plot the data with the explanatory variable on the x-axis and the response on the y – axis. Does a straight line
adequately describe these data? For Y chose “stride” , and for X chose “ Speed”.
A straight line would adequately describe the data represented in this plot. The stride data appears to taper off
once speed hits 22, but for speeds of 15-21, the relationship is nearly a straight line.
b. Calculate r” the correlation coefficients”, interpret r, and find out that its value would support a linear
regression model?
r is the correlation between speed and stride among female runners. A value of 0.994903 suggests a nearly
linear dependency between the two variables. This value would support a linear regression model.
c. Calculate the coefficients of the regression model, and write down the equation of the model. Interpret the
slope of the regression line.
The equation of the model would be ŷ = 1.89255 + 0.07305* speed
The slope of the regression line states that for each unit increase in stride, speed will increase by 0.07305.
d. Add the regression line to the scatter plot.
e. Report the value of r2 , R _ Sq( Coefficient of Determination). What proportion of variation in “Stride” is
explained by the regression?
The coefficient of determination in this situation indicated that the regression model explains 98.9832% of the
variation in stride.
f.
Obtain the fitted values, report the values.
g. Obtain the residuals and verify that the sum of residuals is zero. Report the residuals.
This shows that the sum of residuals is extremely close to zero.
Obtain the diagnostic graphs for the linear regression, see “introduction”, and then answer the following:
h. Check the graph of residuals against the explanatory variable”. What does the plot indicate about the
adequacy of the linear fit? Do you have any suggestions?
The plot indicates an adequate linear fit, as there does not seem to be any distinct trend in the distribution of
points
i.
Use the Q-Q plot, check whether residual errors are normally distributed , and there is no trend in this plot
Application 2:
a. Plot the data with the explanatory variable on the x-axis and the response on the y – axis. Does a straight line
adequately describe these data?
A straight line does not describe this data plot.
b. Calculate r” the correlation coefficients”, interpret r, and find out that its value would support a linear
regression model?
r is the correlation between age and weight amongst newborn babies. A value of 0.9065522 suggest a relatively
high correlation between age and weight. This value would support a linear regression model.
c. Calculate the coefficients of the regression model, and write down the equation of the model. Interpret the
slope of the regression line.
The equation of the model would be ŷ = 4.8803 + 0.0.2671* age
The slope of the regression line states that for each increase in weight, age will increase by 0.2671.
d. Add the regression line to the scatter plot.
e. Report the value of r2 , R _ Sq( Coefficient of Determination). What proportion of variation in “Stride” is
explained by the regression?
The coefficient of determination in this situation indicated that the regression model explains 82.1837% of the
variation in weight.
f.
Obtain the fitted values, report the values.
g. Obtain the residuals and verify that the sum of residuals is zero. Report the residuals.
This shows that the sum of residuals is extremely close to zero.
Obtain the diagnostic graphs for the linear regression, see “introduction”, and then answer the following:
j. Check the graph of residuals against the explanatory variable”. What does the plot indicate about the
adequacy of the linear fit? Do you have any suggestions?
The plot indicates an adequate linear fit, as there does not seem to be any distinct trend in the distribution of
points
k. Use the Q-Q plot, check whether residual errors are normally distributed , and there is no trend in this plot