Final answer:
To decide what type of function best models a dataset, one should analyze the scatter plot of the dependent and independent variables, calculate the least-squares regression line, determine the correlation coefficient, and assess for outliers.
Step-by-step explanation:
To determine whether a dataset is best modeled by a linear, quadratic, exponential, or logarithmic function, one must analyze the relationship between the changes in the independent and dependent variables. This process typically involves plotting the data on a scatter plot and assessing the pattern of the points. If the points form a straight line, the relationship may be linear. A parabolic shape suggests a quadratic relationship, while an exponential function would see either rapid growth or decay. A logarithmic relationship would present a rapid increase or decrease that levels off.
Steps such as calculating the least-squares line (ý = a + bx) and finding the correlation coefficient can further quantify the relationship. A significant correlation coefficient close to 1 or -1 indicates a strong linear relationship. Comparing the estimated values calculated from the regression equation with actual data can help confirm if the model is appropriate. It is also important to check for any outliers that might distort the analysis.