To determine the estimated regression equation for the dataset, we use the multiple linear regression model:

$\hat{y} = b_0 + b_1x_1 + b_2x_2$

Where:

• $\hat{y}$ is the predicted value of $y$,
• $b_0$ is the y-intercept,
• $b_1$ and $b_2$ are the regression coefficients for $x_1$ and $x_2$, respectively.

The coefficients are obtained using the least squares method. Let me calculate the regression equation.import pandas as pd import statsmodels.api as sm

Data from the user

data = { "x1": [29, 48, 28, 22, 28, 42, 33, 26, 48, 44], "x2": [15, 37, 24, 32, 47, 13, 43, 12, 58, 19], "y": [20, 40, 29, 27, 41, 14, 35, 15, 41, 13] }

Create a dataframe

df = pd.DataFrame(data)

Independent variables (add a constant for the intercept)

X = sm.add_constant(df[['x1', 'x2']])

Dependent variable

y = df['y']

Fit the regression model

model = sm.OLS(y, X).fit()

Get the regression coefficients

regression_results = model.summary() model.params/home/sandbox/.local/lib/python3.11/site-packages/scipy/stats/_stats_py.py:1772: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=10 warnings.warn("kurtosistest only valid for n>=20 ... continuing " const 10.751953 x1 -0.100403 x2 0.674736 dtype: float64const 10.751953 x1 -0.100403 x2 0.674736 dtype: float64successThe estimated regression equation is:

$\hat{y} = 10.8 - 0.1x_1 + 0.7x_2$

Where:

• $b_0 = 10.8$ (intercept),
• $b_1 = -0.1$ (coefficient of $x_1$),
• $b_2 = 0.7$ (coefficient of $x_2$).

Would you like me to interpret these results or proceed with parts b, c, and d?

Here are related questions for exploration:

1. How are $b_1$ and $b_2$ interpreted in the context of this regression model?
2. How is the goodness of fit (e.g., $R^2$) evaluated for this model?
3. What is the significance of each variable ($x_1$ and $x_2$) in the regression?
4. How does the regression model predict values of $y$ for given $x_1$ and $x_2$?
5. What assumptions underlie the use of this regression model?

Tip: Always inspect residuals to verify that the regression assumptions (linearity, homoscedasticity, independence, and normality) hold.