qqplot

Use a quantile-quantile plot to determine whether gas prices in Massachusetts follow a normal distribution.

Load the sample data.

load gas

The sample data in price1 and price2 represent gasoline prices at 20 different gas stations in Massachusetts. The samples were collected during two different months.

Create a quantile-quantile plot to determine if the gas prices in price1 follow a normal distribution.

figure
qqplot(price1)

The plot produces an approximately straight line, suggesting that the gas prices follow a normal distribution.

Use a quantile-quantile plot to determine whether two sets of sample data come from the same distribution.

Load the sample data.

load gas

The sample data in price1 and price2 represent gasoline prices at 20 different gas stations in Massachusetts. The samples were collected during two different months.

Create a quantile-quantile plot using both sets of sample data, to assess whether prices at different times have the same distribution.

qqplot(price1,price2);

The plot produces an approximately straight line, suggesting that the two sets of sample data have the same distribution.

Use a quantile-quantile plot to determine whether sample data comes from a Weibull distribution.

Load the sample data.

load lightbulb

The first column of the data has the lifetime (in hours) of two types of light bulbs. The second column has information about the type of light bulb. 1 indicates fluorescent bulbs whereas 0 indicates the incandescent bulbs. The third column has censoring information. 1 indicates censored data, and 0 indicates the exact failure time. This is simulated data.

Remove the censored data.

lightbulb = [lightbulb(lightbulb(:,3)==0,1),...
    lightbulb(lightbulb(:,3)==0,2)];

Create a variable for each light bulb type. Include only uncensored data.

fluo = [lightbulb(lightbulb(:,2)==0,1)];
insc = [lightbulb(lightbulb(:,2)==1,1)];

Create a Weibull probability distribution object using the default parameters of A = 1 and B = 1.

pd = makedist('Weibull');

Create a q-q plot to determine whether the lifetime of fluorescent bulbs has a Weibull distribution.

figure
qqplot(fluo,pd)

The plot is not a straight line, suggesting that the lifetime data for fluorescent bulbs does not follow a Weibull distribution.

Display a side-by-side pair of quantile-quantile plots using the tiledlayout and nexttile functions.

Load the patients data set. Separate the patient diastolic blood pressure levels into two data sets: one containing the diastolic blood pressure levels of smokers and one containing the diastolic levels of nonsmokers.

load patients

smokerIndices = (Smoker == 1);
nonsmokerIndices = (Smoker == 0);

smokerDiastolic = Diastolic(smokerIndices);
nonsmokerDiastolic = Diastolic(nonsmokerIndices);

Create a 2-by-1 tiled chart layout using the tiledlayout function. Create the first set of axes ax1 within the chart layout by calling the nexttile function. In the axes, display a q-q plot to determine whether the diastolic blood pressure levels of smokers come from a normal distribution. Create the second set of axes ax2 within the tiled chart layout by calling the nexttile function. In the axes, display a q-q plot to determine whether the diastolic blood pressure levels of nonsmokers come from a normal distribution.

tiledlayout(2,1)

% Top axes
ax1 = nexttile;
qqplot(ax1,smokerDiastolic)
ylabel(ax1,'Diastolic Quantiles for Smokers')
title(ax1,'QQ Plot of Smoker Diastolic Levels vs. Standard Normal')

% Bottom axes
ax2 = nexttile;
qqplot(ax2,nonsmokerDiastolic)
ylabel(ax2,'Diastolic Quantiles for Nonsmokers')
title(ax2,'QQ Plot of Nonsmoker Diastolic Levels vs. Standard Normal')

The second plot more closely follows a straight line, suggesting that the sample of nonsmoker blood pressure values has an approximately normal distribution. In contrast, the first plot has points below the line to the left, suggesting a heavier tail (more outliers) than a normal distribution.