# Determining The Predictor Variables Of A Predictor Variable Is Very Small For The F Test

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QUESTION 1 Answer (a): According to this problem, the p value is very small for the F test. Hence, the null hypothesis needs to be rejected (Conclusion). This basically means that at least 1 of the predictor variables seems to have a linear relationship with the outcome variable. We don’t know which outcome variable it is. The null hypothesis for this F test says that all slopes of each and every predictor variable in the regression model equal to 0 – this basically means that each of the predictor variable has no linear relationship with the outcome variable. Answer (b): The t tests tell us if the predictor variable has a significant linear association with the outcome variable or not. The alpha value of 0.05 is used; if the value of…show more content…
In Model 2, we can see that it has a better F test but it’s RSE and adjusted R2 value is the same. The regular R2 value and the adjusted R2 value is different because it depends on the number of variables we have in our model. As we know, an R2 value closer to 1 means that the values are good – but that isn’t the case here. Here, the R2 value will definitely increase with an increase in the number of variables, but that does not qualify for the variables to be good (more model parameters  better fit, higher R2). Adjusted R2 formula punishes us for having many numbers (i.e. if we have added more numbers unnecessarily). It shows us the variation in y axis and level of efficiency (with regard to using less variables). Answer (d): The slope in Model 2 (multiple linear regression) shows us the consequences of changing a unit on y axis, while keeping all the x variables constant. For example, if the weight is increased by 1 point, the pemax also increases by 1.64. The bmp remains constant. If the bmp is increased by 1 point, the pemax decreases by 1.005 (weight remains constant). Answer (e): I think that Models 3 and 4 are in consistent with Model 2. According to me, the difference lies in the way we interpret them. There is only 1 variable in Model 3 as well as in Model 4, hence, the interpreted answer misses out on the control of the other variable. Model 3 shows us the consequence of