Final answer:
In this analysis, the dependent variable is brand liking (Y) and the independent variable is sweetness (X2). We can draw a scatter plot of the ordered pairs and calculate the least-squares line to represent the best-fit line for the data. The correlation coefficient between the two sets of residuals can be calculated, and its square equals R Y1∣22, the coefficient of determination.
Step-by-step explanation:
a. In this analysis, brand liking (Y) should be set as the dependent variable, while sweetness (X2) should be set as the independent variable.
b. To draw a scatter plot of the ordered pairs, plot the brand liking values on the y-axis and the sweetness values on the x-axis. Each ordered pair represents a data point on the plot.
c. To calculate the least-squares line, use the SLR model to find the equation of the line in the form ý = a + bx. The equation will represent the best-fit line for the data points.
d. Find the correlation coefficient between the two sets of residuals. The correlation coefficient measures the strength and direction of the linear relationship between the residuals.
e. The coefficient of determination, R Y1∣22, can be calculated by squaring the correlation coefficient. It represents the proportion of the variability in the dependent variable that can be explained by the independent variable.