How could we provide evidence for the positive association between two variables through linear regression model and hypothesis testing? What are the steps?

You are analyzing a dataset with 932 datapoints. You decide to create a linear regression model with this dataset, using 18 predictor variables. Using this information, what is the degrees of freedom associated with the sum of squares total (total sum of squares) of your analysis?

Explain in simple language why knowing only these correlations enables you to say that prediction of manatee deaths from number of boats registered by a regression line will be much more accurate than prediction of a golfer's second‑round score from his first‑round score. Select the correct explanation from the choices.   A) The closer r is to 0 (in either direction), the stronger the linear relationship is between two variables.   B) Actually, prediction of manatee deaths from number of boats registered by a regression line will be much less accurate than prediction of a golfer's second‑round score from his first‑round score.   C) The fraction of the variation in the observed values of x explained by the least‑squares regression of y on x is given by r. The higher this fraction, the more likely that the prediction is accurate.   D) The further r is from 0 (in either direction), the stronger the linear relationship is between two variables.

What are the different ways to reduce the error in least square regression?

what is the regression equation for all predictors? I

Explain about the least square regression line?

True or False? The r2 value and a least squares regression line can be an excellent way to demonstrate the degree of correlation between two variables, and the type of association between the two variables. This quation was asked twice in bartley but the answers were different. Clarification is needed. Thank you

To properly examine the effect of a categorical independent variable in a multiple linear regression model we use an interaction term. True O False

True or false: A proper line regression can be used to predict values of the response variable from absurd values of the explanatory variable.

Provide an example of a regression that arguably would have a high value of R² but would produce biased and inconsistent estimators of a causal effect. Explain why the R² is likely to be high. Explain why the OLS estimators would be biased and inconsistent.