More detail pleas see the file ,total have 8 questions; Now consider a multiple linear regression where the average length of stay in a hospital (Y) is anticipated to be related to infection risk (X1), routine chest X-ray ratio (X2), and available facilities and services (X3).1. (10) Use R to obtain the residual information on the MLR model Y~X1+X2+X3, check assumptions from the residual plot, BF test (you could do a grouping on Y) and Normality test.2.(5) For the MLR model Y~X1+X2+X3, use R to construct the design matrix X and Y, then compute the variance-covariance matrix of the residuals , what is the dimension of the matrix?3. (5) For the MLR model Y~X1+X2+X3, use R to construct the matrix X and Y, then compute the variance-covariance matrix of the parameter estimates , what is the dimension of the matrix? What are the standard error of the parameter estimates?4. (8) Obtain an interval estimate of the mean response when X1=4, X2=81, and X3=43 with 90% confidence level.Specify what are the point estimate, critical value, and the standard error.5. (4) Now consider the interval estimate of the single responsewhen X1=4, X2=81, and X3=43 with 90% confidence level. Without computation, discuss how the point estimate, critical value, and the standard error different are different from question 4.

one Word document for this assignment. You will create this Word document by cutting and pasting SPSS output into Word. Name the file in the following format: lastnamefirstinitialPSY7107-9.doc (example: smithbPSY7107-9.doc).Begin by downloading the following SPSS data setActivity 9.sav (found in Books and Resources for this Week)This week’s assignment consists of two parts. In the first part, you will utilize an existing dataset to compute a factorial ANOVA. All SPSS output should be pasted into your Word document. In the second part, you will be asked to create a hypothetical ANCOVA output table (for variables related to your area of interest). Part A. SPSS AssignmentThe “Activity 9.sav” file contains a dataset of a researcher interested in finding the best way to educate elementary age children in mathematics. In particular, she thinks that 5th grade girls do better in small class sizes while boys excel in larger classes. Through the school district, she has arranged a pilot program in which some classroom sizes are reduced prior to the state-wide mathematics competency assessment. In the dataset, you will find the following variables:Participant: unique identifierGender: Male (M) or Female (F)Classroom: Small (1) – no more than 10 childrenMedium (2) – between 11 and 19 childrenLarge (3) – 20 or more studentsScore – final score on the statewide competency assessment.Now do the following:Exploratory Data Analysis.Perform exploratory data analysis on all variables in the data set. Realizing that you have six groups, be sure that your exploratory analysis is broken down by group. When possible, include appropriate graphs to help illustrate the dataset.Give a one to two paragraph write up of the data once you have done this.Create an APA style table that presents descriptive statistics for the sample.Factorial ANOVA. Perform a factorial ANOVA using the “Activity 9.sav” data set. Is there a main effect of gender? If so, explain the effect. Use post hoc tests when necessary (or explain why they are not required in this specific case).Is there a main effect of classroom size? If so, explain the effect. Use post hoc tests when necessary (or explain why they are not required in this specific case).Is there an interaction between your two variables? If so, using post hoc tests, describe these differences.Is there support for the researcher’s hypothesis that girls would do better than boys in classrooms with fewer students? Explain your answer.Write up the results in APA style and interpret them. Be sure that you discuss both main effects and the presence/absence of an interaction between the two.Part B. Applying Analytical Strategies to an Area of Research InterestBriefly restate your research area of interest.Analysis of Covariance. Using your area of interest, identify one independent and two dependent variables, such that the dependent variables would likely be covariates. Now, assume you conducted an ANCOVA that shows both the first independent variable as well as the covariate significantly predicts the dependent variable. Create a mock ANCOVA output table (see SPSS Output 12.6 in your text for an example) that supports the relationship shown above. Report your mock finding APA style.You should now have the following file:lastnamefirstinitialPSY7107-9.doc (example: smithbPSY7107-9.doc)