The single-step error of Heun's method scales as . In 3-4 sentences, explain what this statement means. Include an example.

You have the following 10 data points recorded in an experiment (x is the independent variable and y is the dependent variable):

You decide to use the built-in Python function nppoly.polyfit() to fit the data with a 9th order polynomial, using the input: p = nppoly.polyfit(x,y,9).

a) Find the value of  for this fit. Give your answer to 2 decimal places.

b) Explain/interpret your  value from the previous question (1 sentence).

c) These data points describe the percentage of surveyed people, y, who have been to the dentist within the last x years. Discuss your interpretation of the fit and what it means for interpolated and/or extrapolated values using this function. Explain your reasoning (2-4 sentences).

Describe two different aspects between closed (bracketed) and open root-finding methods.

For loops and while loops both repeat a set of instructions. Explain the difference between the two loop types. Also, describe when you would use one type over the other.

Copy/paste your code for all parts of the previous question into the textbox below to receive method marks

Copy/paste your code for all parts of the previous question into the textbox below to receive method marks.

Consider a CSV file, data.csv, that contains data about a grocery store's inventory. The dataset contains 3 attributes and many observations. A sample of this dataset is shown below:

Which statement below is true about the midpoint method and Heun’s method for solving ordinary differential equations?

In order to fit an exponential model, , to a set of data, the points in the dataset first need to be transformed. A linear relationship should be seen when you plot: