Question

estimate std.error

Intercept 26184.4 3517.3

snowfall 3824.8 247.5

r^2=.8565

adjusted r^2= .8529

s=8991

1. For each additional inch of snowfall, steam runoff
   1. decreases by 26,184 acre-feet, on average.
   2. increases by 26,184 acre-feet, on average.
   3. .decreases by 3824 acre-feet, on average.  
   4. increases by 3824 acre-feet, on average

1. If multicollinearity is present, then we can conclude that the fitted regression model:
   1. may have estimated slopes very different from what we should expect due to numerical instabilities, making correct interpretation of the effect on the response variable more difficult.
   2. will have a very low r squared value.
   3. is not useful at all and will have a very low r squared value.
   4. may have estimated slopes very different from what we should expect due to numerical instabilities, making correct interpretation of the effect on the response variable more difficult, and contains redundant information due to two or more highly correlated explanatory variables.

2. Which of the following indicates the presence of multicollinearity?
   1. The global F test is statistically significant.

B) R squared is close to 1.

4. At least one VIF value is greater than 10.
5. The standard error for a regression coefficient is smaller than we would expect.

1. Which of the following is NOT true about R-squared in multiple regression?

A) R squared can be artificially increased by adding explanatory variables to the model, even if they are not related to the response variable.

2. R-squared can be equal to 1.
3.         adjusts for the sample size and the number of explanatory variables in the fitted model.

D) r-squared describes the proportion of the variation in the response variable that is explained by the fitted model.

E)    None of the answers is true.

Answer 1

Slope of a regression line or the coefficient of the independent variable is defined as the how much the y value changes when the x value changes by 1 unit. Hence the correct option is option d (positive as the correlation is positive)

Multicollinearity is not useful at all and it will undermine the statistical significance of the low squared variable, thus making low r squared value. Hence the correct option is option c

If one VIF is greater than 1, it is indicative of the presence of multicollinearity. Hence the correct option is at least one VIF value is greater than 10

The following is not true :  r-squared describes the proportion of the variation in the response variable that is explained by the fitted model.

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