Tessa owns a small clothes shop in a seaside town. She records the weekly sales figures, \(\pounds w\), and the average weekly temperature, \(t ^ { \circ } \mathrm { C }\), for 8 weeks during the summer.
The product moment correlation coefficient for these data is - 0.915
Stating your hypotheses clearly and using a \(5 \%\) level of significance, test whether or not the correlation between sales figures and average weekly temperature is negative.
Suggest a possible reason for this correlation.
Tessa suggests that a linear regression model could be used to model these data.
State, giving a reason, whether or not the correlation coefficient is consistent with Tessa’s suggestion.
State, giving a reason, which variable would be the explanatory variable.
Tessa calculated the linear regression equation as \(w = 10755 - 171 t\)
Give an interpretation of the gradient of this regression equation.