Final answer:
To find the best hypothesis function for the data, assess if it follows a linear pattern, consider the presence of outliers, and verify if the linear model holds for all data ranges. The slope of the least-squares line provides a rate of change useful for prediction.
Step-by-step explanation:
Fitting a Hypothesis Function to Data:
To determine what is the best option of the hypothesis function that fits to the data in the graph of the cost function, we must consider the nature of the data presented. When plotting points and assessing the fit of a line, we commonly use the least-squares method to minimize the sum of the squared differences between the observed values and the values predicted by the line. However, whether a line is the best fit is determined by looking at the scatterplot and checking for a linear pattern. If the points roughly follow a straight line trend, a linear function is likely a good model.
Outliers, which are data points that deviate significantly from the rest of the data, can affect the line of best fit. If there are outliers present they may skew the regression line and may need to be considered separately or require a different model altogether. In projection scenarios such as predicting the cost for a 300 oz. size of laundry detergent, the validity of the prediction depends on whether the linear model is a good fit for the entire range of data, including the extrapolation zone. When slope is mentioned in the context of a least-squares line it represents the rate of change in the dependent variable for unit change in the independent variable. An appropriate slope indicates how, for example, costs might increase with each additional ounce of laundry detergent.