James runs a fish and chip shop. He records the average daily temperature, t∘Ct^{\circ}\text{C}t∘C, and the daily sales, £S\pounds S£S, for 10 days in the summer. The product moment correlation for these data is 0.67
Stating your hypotheses clearly and using a 5% significance level, test whether there is a positive correlation between daily sales and daily temperature.
James suggests that a linear regression model could be used to model the data.
State, giving a reason, whether or not the correlation coefficient is consistent with James's suggestion.
State, giving a reason, which variable would be the explanatory variable.
James calculated the linear regression equation as S=5148+141tS = 5148 + 141tS=5148+141t
Give an interpretation of the gradient of this regression equation.
