Regression
Consider a dataset with X values [2, 4, 6, 8] and corresponding Y values [5, 9, 12, 15]. What is the slope (β₁) of the simple linear regression line for this data?
A multiple linear regression model predicts sales (Y) based on two independent variables: advertising expenditure (X₁ in $1000s) and number of salespeople (X₂). If the model equation is Y = 2X₁ + 3X₂ - 10 , and a new data point has X₁ = 5 and X₂ = 8 , what is the predicted sales?
Consider a dataset with X values [3, 5, 7, 9] and corresponding Y values [10, 12, 9, 14]. What is the coefficient of determination (R²) for the simple linear regression model fitted to this data?
A researcher conducts a regression analysis between the number of hours studied (X) and the score obtained in an exam (Y) for a sample of 20 students. The resulting regression equation is Y = 5X + 30. If a student studies for 8 hours, what is the predicted exam score?
A dataset of 15 samples shows a correlation coefficient (r) of -0.68 between two variables X and Y. What does this value indicate about their relationship?