Final answer:
The question involves using linear regression to determine the relationship between two variables, fitting a least-squares line, assessing the correlation coefficient's significance, and establishing if a linear relationship exists for making predictions.
Step-by-step explanation:
The task is to determine the relationship between two variables using linear regression. First, decide which variable is independent (predictor) and which is dependent (response). Then, through data analysis, draw a scatter plot to visualize the potential correlation. Use linear regression to calculate the least-squares line, written as ý = a + bx. Assess the correlation coefficient to gauge the strength and direction of the relationship. The significance of this coefficient indicates if the correlation is strong enough to be considered statistically significant. If it exists, the linear relationship can be used for predictions, such as estimating costs based on distance from campus or predicting average heights for different ages. To confirm the linearity of the data, evaluate whether the line of best fit appropriately represents the data points.
Assuming the role of a restaurant guide analyst, you may use the regression analysis to find the estimated maximum values for restaurants on different pages, examine the placement of high-value restaurants, and extend the model to estimate values for a restaurant on the 200th page. It is important to question if the least-squares line is still valid with extrapolated predictions and to consider the implications of the slope of the line.