is 32, the estimate of the variance of the model errors is
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- The least-squares regression line relating two statistical variables is given as = 24 + 5x. Compute the residual if the actual (observed) value for y is 38 when x is 2. 4 38 2A multiple regression includes two regressors: Yi = b0 + b1X1i +b2X2i + ui. What is the expected change in Y if X1 increases by 8 unitsand X2 is unchanged? What is the expected change in Y if X2 decreasesby 3 units and X1 is unchanged? What is the expected change in Y if X1increases by 4 units and X2 decreases by 7 units?A snack food manufacturer estimates that the variance of the number of grams of carbohydrates in servings of its tortilla chips is 1.25. A dietician is asked to test this claim and finds that a random sample of 22 servings has a variance of 1.35. At ⍶ = 0.05 is there enough evidence to reject the manufacturer’s claim?
- Suppose the simple linear regression model, Yi = β0 + β1 xi + Ei, is used to explain the relationship between x and y. A random sample of n = 12 values for the explanatory variable (x) was selected and the corresponding values of the response variable (y) were observed. A summary of the statistics is presented in the photo attached. Let b1 denote the least squares estimator of the slope coefficient, β1. What is the value of b1?An auto manufacturer claims that the variance of the gas mileage in a model of a hybrid vehicle is 0.16. A random sample of 30 vehicles has a variance of 0.26. At alpha = 0.05, is there enough evidence to reject the claim? Assume the population is normally distributed.Can logistic regression be used in both prospective and retrospective study? Will the odds ratios of the effect of the predictor on the response are different under these two study designs? What formula can we use to solve maximum likelihood estimate of regression coefficient beta in Poisson regression (with log link)? can ridge regression be applied if sample size is smaller than the number of predictors? if any 2 variables in X1, X2 AND Y have a positive correlation, then in the linear regression Y = b0 + b1X1 +b2X2 +e, will the sign of b1 and b2 both be positive? will the residuals that we get from linear regression will always be uncorrelated given X?
- Consider a regression analysis with n = 47 and three potential independent variables. Suppose that one of the independent variables has a correlation of 0.95 with the dependent variable. Does this imply that this independent variable will have a very large Student’s t statistic in the regression analysis with all three predictor variables?A published statistic says that 3% of a certain population have height above 174cm. Suppose the height of the said population is normally distributed with variance 4 sq. cm. What should be the average height of the population (in cm) if the statistic is believed to be true?Please fill in the blanks with appropriate answers. - Of all possible estimators of α and β that are linear in the Yi and unbiased, the least squares estimators that have the smallest variances are said to be………………………….…………….……………………………. according to the…..………………………..……………… theorem. - The ……………………………………… is the proportion of the sample variability of the dependent variable explained by its linear relationship with the independent variable. Thanks.
- 1) Indicate whether the following statements are true or false. Explain why and show your work.a) In a simple regression Yi = B1 + B2 Xi + ui where var(ui) = o^2.X^2, weighting the model by X would solve the problem of non-common (heteroskedastic) variance of the error term.I estimate a multiple linear regression model with two explanatory variables and 255 observations and I find that the RSS is 0.518514. The S.E of the regression is : Select one: a. the square root of the estimated variance of the estimator and it is 0.045361 b. the square root of the estimator of the errors variance and it is 0.045361 c. a measure of precision of the estimates and it is 0.037821 d. a measure of reliability of the estimated coefficients and it is 0.045361 e. the square root of the variance of the estimator and it is 0.0398126Given that age of ECU students is normally distributed. A random sample of 16 students had an average age of 25 years and a variance of 4 square years. The 98% CI for the true average age of all ECU students is?