Define Sharp regression discontinuity designs with example?

A negative correlation between variables X and Y will always result in a positive slope in the linear regression model. Cannot tell from the given information. False True

Tire pressure (psi) and mileage (mpg) were recorded for a random sample of seven cars of thesame make and model. The extended data table (left) and fit model report (right) are based on aquadratic model  Write out the estimated quadratic polynomial regression model.

COmpare and constrast the use of prediction intervals for a Single Linear Regression model having one X and Multiple Linear Regression Model having two predictors X1 and X2. WHat are the similarities/differences in process and interpretation?

What do we mean when we say that a multiple regression model is a multiple linear regression model? What does “linear” mean here? Can we allow any “higher-order terms”? Explain.

Please help me with question d, e, f, g, h, and I. Thank you.

If a regression line for two variables has a small positive slope, then the:  variables are positively associated? variables are negatively associated? association of the variables cannot be determined. variables have no association with each other.

Illustrate the Regression Discontinuity Estimators?

Multiple regression analysis was used to study how an individual's income (Y in thousands of dollars) is influenced by age (X1 in years), level of education (X2 ranging from 1 to 5), and the person's gender (X3 where 1 =female and 0=male). The following is a partial result of a computer program that was used on a sample of 30 individuals.                                    Coefficient        Standard Error                  X1                0.63                         0.094                  X2                0.94                         0.190                  X3                0.52                         0.120               Analysis of Variance             Source of              Degrees             Sum of            Mean             Variation            of Freedom         Squares          Square             F             Regression                                            90             Error                                                   100 Use the above results and write the…

Is it a good idea to make inference using regression in this situation? Chose the answer that is most appropriate: There is a linear trend so using regression is appropriate. Linearity assumption is satisfied. There is a linear trend but regression is not appropriate. Linearity assumption fails. The relationship seems to be curvilinear. Regression is still appropriate because the line seems reasonable. Linearity assumption is satisfied. The relationship seems to be more curvilinear rather than linear. Regression is not appropriate in this situation because the linearity condition fails and the independent random errors condition also fails.