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# Univariate Analysis For Business Research MCOM Sem 4 Delhi University Notes

## Univariate Analysis For Business Research MCOM Sem 4 Delhi University Notes

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### Univariate Analysis For Business Research MCOM Sem 4 Delhi University Notes

Univariate Analysis For Business Research MCOM Sem 4 Delhi University :  Univariate means that you are assuming that the response variable is influenced only by one other factor. Example: SAT scores are influenced by GPA. You may be looking to test the hypothesis that as the GPA rises, the SAT score rises. Here you are assuming that the GPA is the only factor influencing the SAT score.

Multivariate means that you are assuming that the response variable is influenced by multiple factors (and even combinations of factors). So for example, you might assume that SAT scores are influenced by GPA and sex (male or female). This type of analysis also leads to possibilities of crossterms, meaning there is some effect of being male and having a certain GPA on the SAT scores vs being female and having a certain GPA. Basically, a short answer is, univariate deals with 1 predictor variable; multivariate deals with multiple predictor variables.

### Univariate Analysis For Business Research MCOM Sem 4 Delhi University Notes

Univariate Analysis For Business Research MCOM Sem 4 Delhi University : Univariate analysis is perhaps the simplest form of statistical analysis. Like other forms of statistics, it can be inferential or descriptive. The key fact is that only one variable is involved.

#### Many ways to describe business statistically

Univariate:

Example: Pie charts of sales via territory, bar chart of support call volume by products, line charts of profit over several quarters – all of these descriptions involve one variable at a time. They are all considered part of an univariate analysis.

Bivariate:

Example: A presentation of two variables at a time as in a scatter plot. Any analysis that is performed on the scatter plot. Attempt to understand the relationship between sales volume and ad spending. These are all examples of bivariate analysis.

A bivariate analysis may or may not have a target variable. If there is no target variable, then a complete bivariate analysis will involve studying n* (n-1)*0.5 total scatter plots, where n is the number of variables.

Multivariate:

When there are more than one target (or response) variables, any analysis involving studying the effect of predictors on the responses and their interactions is termed multivariate analysis.

### Univariate Analysis For Business Research MCOM Sem 4 Delhi University Notes

Univariate Analysis For Business Research MCOM Sem 4 Delhi University : Univariate analysis is a form of quantitative, statistical, evaluation. This method of analysis separately studies the findings regarding each variable in a data set, and therefore each individual variable is summarized on its own.

#### Univariate Analysis – Market Research

Consequently univariate data does not look at relationships between various variables (like bivariate and multivariate analysis); its sole purpose is to describe one aspect of a piece of research. The easiest way of consolidating the data for one variable is either in a frequency distribution table or bar graph, although other formats can be used (e.g. pie chart, histogram etc.). This means that the number of cases in a particular category (variable) are analysed in one of these chosen means of presentation.

Using the question ‘what’s the age of individuals in the village?’ you may get a wide range of numbers, so the best thing to do is to group the ages (once you have decided on the categories to use) and tally them in a frequency table.

After gathering the data for the particular variable in question a researcher can then determine a number of measures regarding the distribution of the data, including: the median, mean, standard deviation, and the minimum and maximum values. Having these values allows a researcher to carry out a number of tests in order to establish a clearer picture of the distribution of the data.

### Univariate Analysis For Business Research MCOM Sem 4 Delhi University Notes

Univariate Analysis For Business Research MCOM Sem 4 Delhi University : Univariate is a term commonly used in statistics to describe a type of data which consists of observations on only a single characteristic or attribute. A simple example of univariate data would be the salaries of workers in industry. Like all the other data, univariate data can be visualized using graphs, images or other analysis tools after the data is measured, collected, reported, and analyzed.

#### Univariate data types

Some univariate data consists of numbers (such as the height of 65 inches or the weight of 100 pounds), while others are nonnumerical (such as eye colors of black or blue). Generally, the terms categorical univariate data and numerical univariate data are used to distinguish between these types.

#### Categorical univariate data

Categorical univariate data consist non-numerical observations that may be placed in categories. It includes labels or names used to identify an attribute of each element. Categorical univariate data usually use either nominal or ordinal scale of measurement.

#### Numerical univariate data

Numerical univariate data consist observations that are numbers. They are obtained using either interval or ratio scale of measurement. This type of univariate data can be classified even further into two subcategories: discrete and continuousA numerical univariate data is discrete if the set of all possible values is finite or countably infinite. Discrete univariate data are usually associated with counting (such as the number of books read by a person). A numerical univariate data is continuous if the set of all possible values is an interval of numbers. Continuous univariate data are usually associated with measuring (such as the weights of people).

### Univariate Analysis For Business Research MCOM Sem 4 Delhi University Notes

Univariate Analysis For Business Research MCOM Sem 4 Delhi University :  Univariate analysis is the simplest form of analyzing data. Uni means one, so in other words the data has only one variable. Univariate data requires to analyze each variable separately. Data is gathered for the purpose of answering a question, or more specifically, a research question. Univariate data does not answer research questions about relationships between variables, but rather it is used to describe one characteristic or attribute that varies from observation to observation. Usually there are two purposes that a researcher can look for. The first one is to answer a research question with descriptive study and the second one is to get knowledge about how attribute varies with individual effect of a variable in Regression analysis. There are some ways to describe patterns found in univariate data which include graphical methods, measures of central tendency and measures of variability.

### Graphical methods

The most frequently used graphical illustrations for univariate data are:

#### Frequency distribution tables

Frequency is how many times a number occurs. The frequency of an observation in statistics tells us the number of times the observation occurs in the data. For example, in the following list of numbers {1, 2, 3, 4, 6, 9, 9, 8, 5, 1, 1, 9, 9, 0, 6, 9}, the frequency of the number 9 is 5 (because it occurs 5 times).

#### Bar charts

This is an example of barplot.

Bar chart is a graph consisting of rectangular bars. There bars actually represents number or percentage of observations of existing categories in a variable. The length or height of bars gives a visual representation of the proportional differences among categories.

#### Histograms

histogram

Histograms are used to estimate distribution of the data, with the frequency of values assigned to a value range called a bin.

#### Pie charts

Pie chart is a circle divided into portions that represent the relative frequencies or percentages of a population or a sample belonging to different categories.

#### Measures of central tendency

Central tendency is one of the most common numerical descriptive measures. It’s used to estimate the central location of the univariate data by the calculation of mean, median and mode. Each of these calculation has its own advantages and limitations.The mean has the advantage that its calculation includes each value of the data set, but it is particularly susceptible to the influence of outliers. The median is a better measure when the data set contains outliers. The mode is simple to locate. The important thing is that it’s not restricted to using only one of these measure of central tendency. If the data being analyzed is categorical, then the only measure of central tendency that can be used is the mode. However, if the data is numerical in nature (ordinal or interval/ratio) then the mode, median, or mean can all be used to describe the data. Using more than one of these measures provides a more accurate descriptive summary of central tendency for the univariate.

#### Measures of variability

A measure of variability or dispersion (deviation from the mean) of a univariate data set can reveal the shape of a univariate data distribution more sufficiently. It will provide some information about the variation among data values. The measures of variability together with the measures of central tendency give a better picture of the data than the measures of central tendency alone. The three most frequently used measures of variability are range, variance and standard deviation.

### Univariate Analysis For Business Research Mcom Sem 4 Delhi University Notes

Univariate Analysis For Business Research Mcom Sem 4 Delhi University :

The UNIVARIATE procedure provides the following:

• descriptive statistics based on moments (including skewness and kurtosis), quantiles or percentiles (such as the median), frequency tables, and extreme values
• histograms that optionally can be fitted with probability density curves for various distributions and with kernel density estimates
• cumulative distribution function plots (cdf plots). Optionally, these can be superimposed with probability distribution curves for various distributions.
• quantile-quantile plots (Q-Q plots), probability plots, and probability-probability plots (P-P plots). These plots facilitate the comparison of a data distribution with various theoretical distributions.
• goodness-of-fit tests for a variety of distributions including the normal
• the ability to inset summary statistics on plots
• the ability to analyze data sets with a frequency variable
• the ability to create output data sets containing summary statistics, histogram intervals, and parameters of fitted curves

You can use the PROC UNIVARIATE statement, together with the VAR statement, to compute summary statistics. See the section Getting Started: UNIVARIATE Procedure for introductory examples. In addition, you can use the following statements to request plots:

• the CDFPLOT statement for creating cdf plots
• the HISTOGRAM statement for creating histograms
• the PPPLOT statement for creating P-P plots
• the PROBPLOT statement for creating probability plots
• the QQPLOT statement for creating Q-Q plots
• the CLASS statement together with any of these plot statements for creating comparative plots
• the INSET statement with any of the plot statements for enhancing the plot with an inset table of summary statistics

The UNIVARIATE procedure produces two kinds of graphical output:

• traditional graphics, which are produced by default
• ODS Statistical Graphics output, which is produced when you specify the ODS GRAPHICS statement prior to your procedure statements statements.

### Example:

An ice cream shop keeps track of how much ice cream they sell versus the temperature on that day.

The two variables are Ice Cream Sales and Temperature.

Here are their figures for the last 12 days:

Temperature °C Ice Cream Sales Ice Cream Sales vs Temperature 14.2° \$215 16.4° \$325 11.9° \$185 15.2° \$332 18.5° \$406 22.1° \$522 19.4° \$412 25.1° \$614 23.4° \$544 18.1° \$421 22.6° \$445 17.2° \$408

And here is the same data as a Scatter Plot:

Now we can easily see that warmer weather and more ice cream sales are linked, but the relationship is not perfect.

### Univariate Analysis For Business Research MCOM Sem 4 Delhi University Notes

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