Let's break down each part of this problem step by step.

A. r = Pearson Correlation Coefficient

The Pearson correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. It can be calculated using the formula:

[ r = \frac{n \sum{xy} - (\sum{x})(\sum{y})}{\sqrt{[n \sum{x^2} - (\sum{x})^2][n \sum{y^2} - (\sum{y})^2]}} ]

Where:

• $n$ is the number of data points (in this case, 11 pairs),
• $x$ represents the time spent,
• $y$ represents the money spent.

I'll calculate $r$ for you. Let me process the values. numpy as np

Given data

time_spent = np.array([18, 24, 9, 32, 12, 17, 22, 28, 15, 21, 19]) money_spent = np.array([31, 30, 26, 79, 24, 37, 45, 88, 22, 35, 25])

Calculate Pearson correlation coefficient

r = np.corrcoef(time_spent, money_spent)[0, 1] r### A. r = 0.814

The Pearson correlation coefficient $r$ is approximately 0.814, which indicates a strong positive linear relationship between the amount of time spent in the store and the amount of money spent.

B. r² = Coefficient of Determination

The coefficient of determination $r^2$ represents the proportion of the variance in the dependent variable that is predictable from the independent variable. It is calculated as:

$r^2 = (r)^2$

Let me calculate $r^2$. Calculate r^2 r_squared = r**2 r_squared### B. r² = 0.662

The coefficient of determination $r^2$ is approximately 0.662. This means that about 66.2% of the variability in the money spent is explained by the amount of time spent in the store.

C. Equation of the Least Squares Regression Line

The equation of the least squares regression line is given by:

$y = a + bx$

Where:

• $b = \frac{n \sum{xy} - (\sum{x})(\sum{y})}{n \sum{x^2} - (\sum{x})^2}$ is the slope,
• $a = \frac{\sum{y} - b \sum{x}}{n}$ is the y-intercept.

I'll calculate the equation for you now. Calculate slope (b) and intercept (a) for the regression line n = len(time_spent) sum_x = np.sum(time_spent) sum_y = np.sum(money_spent) sum_x_squared = np.sum(time_spent**2) sum_xy = np.sum(time_spent * money_spent)

Calculate slope (b)

b = (n * sum_xy - sum_x * sum_y) / (n * sum_x_squared - sum_x**2)

Calculate intercept (a)

a = (sum_y - b * sum_x) / n

a, b### C. Equation of the Least Squares Regression Line

The equation of the least squares regression line is:

$y = -13.547 + 2.724x$

Where:

• $y$ is the money spent,
• $x$ is the time spent in minutes.

D. Prediction for 20 Minutes of Shopping

To predict the amount of money spent when a person spends 20 minutes in the store, we can plug $x = 20$ into the regression equation:

$y = -13.547 + 2.724(20)$

Let's calculate that. Predict money spent when time is 20 minutes time_20 = 20 predicted_money_20 = a + b * time_20 predicted_money_20It seems like I can’t do more advanced data analysis right now. Please try again later. However, I can still provide further explanations or assist with any other part of the question. Let me know how you would like to proceed!