Linear Regression FiniteQuest linear regression model

Linear Regression

Quantitative Methods

1 / 10

In a simple linear regression model, you have the following data points for the independent variable (X) and dependent variable (Y):

X: [2, 4, 6, 8, 10]

Y: [5, 7, 8, 12, 15]

What is the slope (a) of the regression line in this model?

1.25

1.5

1.1

2.15

2 / 10

Which of the following is not a common assumption of linear regression?

Linearity

Independence of errors

Normal distribution of independent variables

Constant variance of errors

3 / 10

When interpreting the coefficient of an independent variable in a linear regression model, what does a positive coefficient indicate?

There is no relationship between the independent and dependent variables.

An increase in the independent variable is associated with a decrease in the dependent variable.

An increase in the independent variable is associated with an increase in the dependent variable.

It has no effect on the interpretation.

4 / 10

What is the purpose of the coefficient of determination (R-squared) in linear regression?

It measures the strength of the relationship between independent and dependent variables.

It measures the accuracy of the model’s predictions.

It measures the proportion of variance in the dependent variable explained by the independent variables.

It measures the p-value of the model’s coefficients.

5 / 10

Which of the following is a common assumption of linear regression?

Homoscedasticity

Heteroscedasticity

Multicollinearity

Overfitting

6 / 10

What is the range of values for the correlation coefficient (r) in linear regression?

-1 to 1

0 to 1

-∞ to ∞

0 to 100

7 / 10

Which method is commonly used to find the best-fitting line in linear regression by minimizing the sum of squared errors?

Least Squares Method

Gradient Descent

Maximum Likelihood Estimation

K-Means Clustering

8 / 10

What is the equation for a simple linear regression model with one independent variable (X) and one dependent variable (Y)?

Y = aX + b

Y = aX^2 + bX + c

Y = aX + bX^2 + c

Y = aX^2 + b

9 / 10

In simple linear regression, how many independent variables are used to predict the dependent variable?

None

One

Two

Multiple

10 / 10

What is the primary goal of linear regression?

Classification

Clustering

Prediction

Feature selection

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