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Show that the maximum likelihood estimation for the error variance oin linear regression is given by:
(see attached)
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Looking at Step 2, I'm really confused. You say and true value of the response variable
- Use RStudio to fit a simple linear regression model to the data below. Please submit a copy of your code and any appropriate output (a photo/screenshot will be sufficient). 300? Is the fitted linear regression model What is the 95% prediction interval for xo = appropriate for this data, and which assumption appears to be violated if not? dataset <- data.frame ( с (294, 247, 267, 358, 423, 311, 450, 534, 438, 688, 630, 709, 627, 1021, 615, 700, 999, 1250, 1015, 850, 980, 1650, 1025, 1200, 1500), у 3 с (30, 32, 37, 44, 47, 49, 56, 62, 68, 80, 84, 88, 97, 97, 100, 106, 109, 112, 117, 128, 130, 135, 160, 180, 210) X = %3DA student used multiple regression analysis to study how family spending (y) is influenced by income (x) family size (x2), and addition to savings(x3). The variables y, x1, and x3. The variables y, x1, and x3 are measured in thousands of dollars . The following results were obtained. ANOVA df SS Regression 3 45.9634 Residual 11 2.6218 Total Coefficient Standard Error Intercept 0.0136 X1 0.7992 0.074 X2 0.2280 0.190 X3 -0.5796 0.920 Write out the estimated regression equation for the relationship between the variables. Compute coefficient of determination. What can you say about the strength of this relationship? Carry out a test to determine whether y is significantly related to the independent variables. Use a 5% level of significant. Carry out a test to see if X3 and y are significantly related. Use a 5% level of significancePlease do not explain, just say the answer like A,B,C,D,
- Suppose we have fit a multiple linear regression with 8 explanatory variables and an intercept with 85 observations. We want to test the joint significance of the first 5 explanatory variables using an F test. Please fill in the blanks for the numerator and denominator degrees of freedom of the F statistic of the test: "The F statistic is F(Suppose that I want to estimate the effect of x₁ on y. Consider the univariate regression line: how to calculate a and b₁ using OLS? y = a + b₁x₁A linear regression model based on a random sample of 36 observations on the response variable and 4 predictors has a multiple coefficient of determination equal to 0.697. What is the value of the adjusted multiple coefficient of determination?
- The accompanying scatterplot shows the relationship between the age of an internet user and the amount of time spent browsing the internet per week (in minutes). The accompanying residual plot is also shown along with the QQ plot of the residuals. Choose the statement that best describes whether the condition for Normality of errors does or does not hold for the linear regression model. Choose the statement that best describes whether the condition for Normality of errors does or does not hold for the linear regression model. A.The residual plot displays a fan shape; therefore the Normality condition is not satisfied.B.The QQ plot mostly follows a straight line; therefore the Normality condition is satisfied.C.The scatterplot shows a negative trend; therefore the Normality condition is satisfied.D.The residual plot shows no trend; therefore the Normality condition is not satisfied.Consider a simple regression Y = B1 + B2 X + u. Suppose we found out that the variance of error term is changing with larger values of X (heteroscedasticity). Show how you overcome the problem of heteroscedasticity by using White’s heteroscedasticity consistent variances (only for variance of the slope estimate). Show and explain.A group of Maternal and Child Health public health practitioners are interested in the relationship between depression and a number of health outcomes. Suppose the research team gathers information on a group of participants, and constructs a multiple linear regression model looking at the relationship between depression and household income dichotomized as above and below the federal poverty line controlling for a number of potential confounders. The following is a computerized output displaying the results of their analysis. Parameter Estimate Standard Error t Value Pr > |t| Intercept 0.2617346843 0.09209917 2.84 0.0046 Income (1/0) -.1962038300 0.04574793 -4.29 <.0001 Race (W or AA) -.0320329506 0.03900447 -0.82 0.4118 bmicontinuous 0.0051185980 0.00216986 2.36 0.0186 Alcohol (Y/N) -.0088735044 0.03090631 -0.29 0.7741 A) What are the independent and dependent variables? B) Which potential…
- Please do not give solution in image format thankuIS the following statment true or false, please explain why For each x term in the multiple regression equation, the corresponding β is referred to as a partial regression coefficient.Write down the null and the alternative hypothesis to test the absence of first order autocorrelation assumption of the classical linear regression model