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The value of the correlation coefficient always ranges from:

- O -1 and 0
- O 0 and 1
- O -1 and 1

What is the purpose of the `fit()` method in sklearn?

- O `fit()` method is used to find the intercept in your model
- O `fit()` method is used to train your model
- O `fit()` method is used to predict your model

Two data scientists present you with fits of their linear regression model for predicting house prices from square feet. You notice the slope and the estimated intercepts are the same. Does it imply that the two data scientists fit their models on exactly the same dataset?

- O False
- O True

The average price of a house in a certain neighborhood is modeled by the following regression line: [tex]y = 144x + 45000[/tex], where [tex]x[/tex] represents the square footage of the house. What is the predicted value of a house that is 3500 square feet?

- O 549,000
- O 545,000
- O 544,000
- O 550,000

Which of the following statements is true for a linear regression model?

- O MSE does not reflect the accuracy of the model.
- O The lower the value of MSE, the better the model is.
- O The higher the value of MSE, the better the model is.
- O Clustering analysis is performed by linear regression.

Question 3 (10 pts): Which of the following statements is not true about linear regression?

- O Linear regression uses a straight line for estimation.
- O In linear regression, the target (output) is a linear combination of input variables (features).
- O Linear regression is used in supervised learning.
- O In a linear regression model, there is only one input and multiple output values.

Answer :

The correlation coefficient ranges from -1 to 1, fit() method trains models, same slope doesn't mean same dataset, predicted value for 3500 sqft is 549,000, lower MSE is better in linear regression. Linear regression does not have only one input and multiple outputs.

1. The value of the correlation coefficient ranges between (c) -1 and 1. The correct option is (c). It indicates the strength and direction of the linear relationship between two variables. A value of -1 indicates a perfect negative linear relationship, 1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship.

2. The fit() method in sklearn (b) is used to train your model. The correct option is (b).

The fit() method in sklearn (b) is used to train a machine learning model. During training, the model learns from the input data and adjusts its parameters to make accurate predictions on new, unseen data. It finds the optimal values for the model's parameters to minimize the difference between predicted and actual values.

3. The statement "Two data scientists present you with fits of their linear regression model for predicting house prices from square feet. You notice the slope and the estimated intercepts are the same" is False. The correct option is (a).

Having the same slope and estimated intercepts in linear regression models does not necessarily mean that the data scientists used the same dataset. These coefficients are determined by the optimization process, and even different datasets with similar characteristics can lead to similar coefficients.

4. Using the given regression line y = 144x + 45000, when the house's square footage is 3500, the predicted value of the house is calculated as 144 * 3500 + 45000 = 549,000 (a). The correct option is (a).

5. The statement (b) "The lower the value of MSE, the better the model is" not true. The correct option is (b). The Mean Squared Error (MSE) is a metric used to evaluate the performance of a linear regression model. A lower MSE indicates that the model's predictions are closer to the actual values, making it a better fit for the data.

6. The statement (d) " In linear regression model, there is only one input and multiple output values" is not true. The correct option is (d).

Linear regression does not have a restriction of having only one input and multiple output values. It can have multiple input features and a single output variable, making predictions based on a linear combination of those features.

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