Question

TABLE 1: STATISTICS RESULTS FOR POPULATION DATA Fruit & Veggie % Colorectal Cancer Rates POPULATION SIZE (# of Kentucky counties) MEAN STANDARD DEVIATION 120 9.5 4.56 120 52.78 10.04 TABLE 2: LINEAR REGRESSION RESULTS 0.08419 0.007088 r-value R squared value p-value Regresson Equation 4.29e-50 or< y--0.1852x54.541

i need help understanding and interpreting what this graph means... what exactly does it tell about the x & y variables?

also what do these values for r, r-squared, p-value and regression equation mean for the data?

Answer 1

Solution-

Graph shows the fitted regression line in the scatter plot of data. As we see that data points are well scattered and does not seem to be in a straight line, we can deduce that the variables do not seem to be linearly related.

Regression equation is-

Y = 54.541 - 0.1852 X

Slope = -0.1852, This means that when value of X increases by 1 unit, then Y falls by 0.1852 units and vice versa.

Intercept = 54.541, This means that when X = 0, then expected value of Y = 54.541

value of R² = 0.007

This means that only 0.7% of the total variation in the dependent variable is explained by the independent variable.

As this value is very much low, we can say that linear model is not a good fit here.

P-value is here to test the validity of the model and hypotheses-

H0 - Model is invalid

Ha- Model is valid

As p-value < 0.05, we can say that null hypothesis is rejected at 5% level of significance and we can say that model is valid here.

Thanks!