Page 2 QUESTION ONE The following table shows the hours of sunshine, x, during nine days in August and the number of ice creams sold at a beach shop in Cornwall. x 4.3 6.9 0.0 10.4 5.2 1.8 8.0 9.2 2.1 y 224 208 123 419 230 184 362 351 196 a. Estimate a simple linear regression model and find the value of the parameters for the estimation of ice cream sold from the hours of sunshine. [6 marks] b. Interpret the intercept and the slope coefficients [2 marks] c. Estimate the number of ice creams sold when the hours of sunshine are: [4 marks] i. 8.2 ii. 4.8 d. Compute the correlation coefficient and the coefficient of determination. [3 marks] QUESTION TWO A group of respondent were asked to indicate their preference for three photographs of adults. Do the data suggest that there is a significant relationship between age and photograph preference Photograph A Photograph B 5-9 10-14 15-19 18 22 2 28 20 10 Photograph C 20 40 40 a. State both the null and alternative hypotheses. [2 marks] b. Provide the decision rule for making this decision. Use an alpha level of 5%. [2 marks] c. Show all of the work necessary to calculate the appropriate statistic. [5 marks] d. What conclusion are you allowed to draw? [2 marks] e. Would your conlcusion change at the 10% level of significance? [4 marks] QUESTION THREE The St. Lucian Tourist Board conducted a study to see if tourists' overall destination satisfaction is influenced by their nationality, their satisfaction with restaurants and their satisfaction with prices. Data collected on 50 tourists treated as a random sample has been analyzed. The tables below represent the SPSS multiple regression output. Assume that there are no violations of assumptions. Model Model Summary R R Square 133 Adjusted R Square 121 Std. Error of the Estimate .902 a. Predictors: (Constant), Satisfaction with Restaurants, Nationality of Tourist, Satisfaction with Prices in Destination ANOVA Model Sum of Squares dif 1 Regression Residual Total 27.068 3 Mean Square 9.023 F Sig. 11.092 .000 175.709 216 .813 202.777 219 a. Predictors: (Constant), Satisfaction with Restaurants, Nationality of Tourist, Satisfaction with Prices in Destination b. Dependent Variable: Overall satisfaction with the destination Coefficients Unstandardized Coefficients Standardized Coefficients Model B Std. Error Beta (Constant) 1.898 354 5.355 Sig .000 Nationality of Tourist 533 .131 259 4.052 .000 Satisfaction with .008 .039 .013 204 .838 Prices in Destination Satisfaction with 273 .068 253 3.987 .000 Restaurants a. Dependent Variable: Overall satisfaction with the destination a. Determine the multiple regression equation for the data. [3 marks] b. Interpret the coefficient of determination. [2 marks] c. At the 5% significance level, determine if the model is useful for predicting tourists' overall destination satisfaction. In responding, construct and test any appropriate hypothesis. [5 marks] d. At the 5% significance level, does it appear that tourists' satisfaction with restaurants or their satisfaction with prices can be removed from the model as unnecessary? In responding, construct and test any appropriate hypothesis. [5 marks]