Question C

Inspired by a Canadian study that suggests that commuters cycling to work are the happier, a researcher from Melboume investigated the effects of taking the bike to work. One aspect they are interested is a possible relationship between happiness and time spent commuting on a bike. For a sample of 25 participants who cycle to work, the weekly time spend on the bike commuting (WBC) to work is correlate with the results from a happiness questionnaire (HQ). After entering the data into R! a correlation analysis and a linear model was performed with the following results: > contest(HQ,WBC) Pearson's product-moment correlation data: HQ and WBC t = 1.9708, of = 23, p-value = 0.0609 alternative hypothesis: true correlation is not equal to e 95 percent confidence interval: -0. 01769297 8. 67399984 sample estimates: cor 0.3800952 Call : Im (formula = HQ - WBC) Residuals: Min 10 Median 30 Max -28.730 -10.235 -1.859 9.270 30.518 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 30.7993 6. 8602 4.490 0.080166 *## WBC 1. 8119 0.9194 1.971 0.060908 Signif. codes: pow 0.091 3 0.01 "' 9.05 '.' 0.1 ' ' 1 Residual standard error: 14.12 on 23 degrees of freedom Multiple R-squared: 0.1445, Adjusted R-squared: 0.1073 F-statistic: 3.884 on 1 and 23 DF, p-value: 0.0609 Question a. Based on this analysis, what can be said about the relation between HQ and WBC? Question b. The 95% confidence interval of the correlation analysis suggests: Question c. What is the estimated regression equation?: Question d. Based on the estimated regression equation, what is the expected value of HQ for a person a WBC of 9?: Question e. Interpret the relationship between HQ and WBC, based on this analysis: Question f. Which of the following is true: a. WBC and HQ are not significantly correlated. b. We can be 95 percent confident that the coefficient of correlation between WBC and HQ lies betv HQ = 30.799*WBC + 1.812 # HQ = 1.812*WBC + 30.799 e. HQ = 30.799*WBC + 1.812 inferred between WBC and HQ because the assumptions of the te WBC = 30.799*HQ + 1.812 f. WBC = 1.812*HQ + 30.799 e are significantly greater than zero