An agricultural scientist measures the amount of fertilizer applied, f f\,f kg per hectare, and the resulting wheat yield, Y Y\,Y tonnes, for 15 experimental plots. The product moment correlation coefficient for these data is 0.61.
Stating your hypotheses clearly and using a 5% significance level, test whether there is a positive correlation between fertilizer amount and wheat yield.
The scientist 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 the scientist's suggestion.
State, giving a reason, which variable would be the explanatory variable.
The scientist calculated the linear regression equation as Y=4.1+0.05fY = 4.1 + 0.05fY=4.1+0.05f
Give an interpretation of the gradient of this regression equation.