# Multivariate Data Analysis( Short computational exercise)

Load the data into the SPSS statistics software package, and answer the following questions.
1. Is there any evidence of an association between occupational status and the number of visits to the Gymnasium during the past four weeks? Carry out an appropriate hypothesis test.
2. Is there any evidence that the average customer satisfaction score is age-dependent? Carry out an appropriate hypothesis test.
3. The Gymnasium management have calculated that a monthly membership fee of at least £75 will be required to cover the investment and running costs of the upgraded Gymnasium. Test the null hypothesis that the mean willingness-to-pay for membership of the upgraded Gymnasium is at least £75, against the one-sided alternative hypothesis that the mean willingness to pay is less than £75.
4. Test whether there is any evidence of a difference between the willingness-to-pay for membership of the upgraded Gymnasium of male and female customers.
5. Estimate a two-variable linear regression to describe the relationship between household weekly net income and willingness-to-pay for membership of the upgraded Gymnasium. According to this regression, what is the estimated willingness-to-pay of a customer with a household weekly net income of £300?
6. Estimate a multiple regression in which willingness-to-pay for membership of the upgraded Gymnasium is explained by the following characteristics: gender (male/female), occupational status, and household weekly net income.
(i) Comment on the significance of each of these characteristics as determinants of willingness-to-pay.
(ii) Comment briefly on the comparison between the multiple regression estimated in Q6 and the two-variable linear regression estimated in Q5.
(iii) What is the estimated willingness-to-pay of a male self-employed customer with a household weekly net income of £500?
(iv) What is the estimated willingness-to-pay of a female employed customer with a household weekly net income of £400?