# Bivariate Analysis

**Topics:**Statistics, Variance, Statistical hypothesis testing

**Pages:**6 (2033 words)

**Published:**April 13, 2013

Contingency table

In this case, we use contingency table to analyze the relationship between 2 qualitative variables. And this test works by comparing expected and observed frequencies with x2 distribution.

Correlation coefficient

When we need to test the relationship between 2 quantitative variables, we use correlation coefficient and it measured by standardized covariance measure and investigates linear dependence. Before doing this, it is better to first make a scatterplot to check the outliers and linearity then get the idea about the nature and strength relationship. Next, we should calculate the r for correlation coefficient of variation, which measures the degree of linear dependence. r is always in between -1 and +1. If r < 0 or >0, then it is negative or positive linear dependence. if r equal to 0, then no linear dependence. if r equal to 1 or -1, then it is perfect linear dependence. Rating- Price

This scatterplot does not show any clear relationship between the two variables. By using SPSS, we get the Pearson’s correlation coefficient to be r= 0.491, Pvalue=0.00. The Tobs=22.40, which is higher than the critical value of 2.32. In this case, we can reject H0 at 1% significance level. Therefore, we can conclude that there is a strong positive relationship between rating and price, which means that the more rating hotel gets, the higher price will become. Stars- Price

Again, the scatterplot does not show any clear relationship between two variables. And we get the Pearson’s correlation coefficient to be r= 0.592, Pvalue=0.00. The Tobs=29.57, which is higher than the critical value of 2.32. This is the same as what we expected before, there is a strong positive relationship between stars and price. Position- Price

The scatterplot does not show linear relationship between position and price. And we get Pearson’s correlation coefficient to be r= -004, Pvalue=0.880. The Tobs= -0.161, which is higher than the critical value of -2.32. Since r is very close to 0, there is not linear relationship between position and price. Therefore, there is no association between position and price. Position- rating

There is no linear relationship showing by scatterplot. And by using SPSS, we get the Pearson’s correlation coefficient is r=0.012, Pvalue=0.630. The Tobs=-0.477, which is higher than the critical value of -2.32. Since r is really close to 0, there is not relationship between star and position.

T-test

In this section, we are going to analyze the relationship between one qualitative variable (with two categories) and one quantitative variable. Once again, we need to make the scatterplot and compute the F-test for equal variances. When Fobs > Fn1-1, n2-1, α/2, the H0 is rejected; because there is not enough evidence to support that the variances are equal at the given significance level. And H0 is rejected when Tobs > Tv,α or < - Tv,α or p < α,because there is not enough evidence to prove that the means are equal at the given significance level. Restaurant – price

Firstly we make a scatterplot to see whether there are outliers between restaurant and price, but it shows none. By using SPSS, the mean of price differs between hotels that weather they have a restaurant or not. We inferred that the variance of price is bigger for the hotels that have restaurant (F= 2.75). The research has shown that on average hotels that have restaurant are higher in price than the hotels that do not have restaurant. The sample difference of means is equal to -56.741 (Ts=-14.056, p=0.00). The results indicate that there is a positive relationship between restaurant and price, and imply that hotels that have restaurants have higher price than hotels that do not have restaurant. Promotion- price

Once again, the scatterplot does not show linear relationship between promotion and price. With SPSS, the mean of price differs slightly between hotels weather they have promotion or not. We inferred...

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