DISCUSSION 1: In this discussion you will be interpreting output from your Python Scripts for the Module Six Discussion. If you did not complete the Module Six discussion, please complete that before working on this assignment.Last week’s discussion involved development of a multiple regression model that used miles per gallon as a response variable. Weight and horsepower were predictor variables. You performed an overall F-test to evaluate the significance of your model. This week, you will evaluate the significance of individual predictors. You will use output of Python script from Module Six to perform individual t-tests for each predictor variable. Specifically, you will look at Step 5 of the Python script to answer all questions in the discussion this week.In your initial post, address the following items:Is at least one of the two variables (weight and horsepower) significant in the model? Run the overall F-test and provide your interpretation at 5% level of significance. See Step 5 in the Python script. Include the following in your analysis:Define the null and alternative hypothesis in mathematical terms and in words.Report the level of significance.Include the test statistic and the P-value. (Hint: F-Statistic and Prob (F-Statistic) in the output).Provide your conclusion and interpretation of the test. Should the null hypothesis be rejected? Why or why not?What is the slope coefficient for the weight variable? Is this coefficient significant at 5% level of significance (alpha=0.05)? (Hint: Check the P-value, , for weight in Python output. Recall that this is the individual t-test for the beta parameter.) See Step 5 in the Python script.What is the slope coefficient for the horsepower variable? Is this coefficient significant at 5% level of significance (alpha=0.05)? (Hint: Check the P-value, , for horsepower in Python output. Recall that this is the individual t-test for the beta parameter.) See Step 5 in the Python script.What is the purpose of performing individual t-tests after carrying out the overall F-test? What are the differences in the interpretation of the two tests?What is the coefficient of determination of your multiple regression model from Module Six? Provide appropriate interpretation of this statistic. Be sure to clearly communicate your ideas using appropriate terminology. DISCUSSION 2Use the link in the Jupyter Notebook activity to access your MODULE 8 DISCUSSION Python script. In this discussion, you will apply the statistical concepts and techniques covered in this week's reading about one-way analysis of variance (ANOVA). An investment analyst is evaluating the 10-year mean return on investment for industry-specific exchange-traded funds (ETFs) for three sectors: financial, energy, and technology. The analyst obtains a random sample of 30 ETFs for each sector and calculates the 10-year return of each ETF. The analyst has provided you with this data set. Run Step 1 in the Python script to upload the data file.Using the sample data, perform one-way analysis of variance (ANOVA). Evaluate whether the average return of at least one of the industry-specific ETFs is significantly different. Use a 5% level of significance.In your initial post, address the following items:Define the null and alternative hypothesis in mathematical terms and in words.Report the level of significance.Include the test statistic and the P-value. See Step 2 in the Python script.Provide your conclusion and interpretation of the test. Should the null hypothesis be rejected? Why or why not?Does a side-by-side boxplot of the 10-year returns of ETFs from the three sectors confirm your conclusion of the hypothesis test? Why or why not? See Step 3 in the Python script.Finally, be sure to review the Discussion Rubric (ATTACHED) to understand how you will be graded on this assignment.

Answer the following questions. Copy and paste any required data charts or summaries into this Word document. Use additional space as needed. Be sure to include your name on the document and use the file naming convention. Two-way ANOVA A researcher is comparing the effects of 2 different asthma drugs on test performance. The researcher suspects that at least one of the drugs may have a different effect on fresh versus tired test takers. Data was collected on test results achieved by fresh and tired test takers after using each of the 2 drugs. There is concern that the exposure to these drugs could impair more than a person’s ability to take a test and therefore become a Public Health issue. The Research Question is: Does Drug A or Drug B impair test performance in either fresh or tired test takers? Please answer this question using the ANOVA (SPSS document) dataset and the following steps: Multiple Linear Regression A health department randomly selected 400 subjects from a local community and monitored their cardiovascular condition. Data from this study are provided in the Linear and Logistic (SPSS document) dataset. The following variables are included in the database: sex, age, BMI, SBP, DBP, serum cholesterol, coronary heart disease, and follow-up. Multiple Logistic Regression Use the Linear and Logistic (SPSS document) dataset to assess the impact of sex, age, and BMI on the risk of coronary heart disease. Cox Proportional Hazard The Linear and Logistic (SPSS document) dataset, used in problems III and IV, also includes follow-up time (in days) from the beginning of the study to either onset of coronary heart disease or end of the study. This allows you to also look at the relationship of sex to CHD using survival analysis techniques. Provide numeric descriptive statistics (include skewness and kurtosis if appropriate) and graphic descriptions for Alertness, Drug Treatment, and Test Performance. Create histograms of the test performance results (dependent variable) for each combination of levels for the two independent variables. Describe the data and shape of the distributions. Discuss whether the assumptions of homogeneity of variance of the groups and normality of the data on test performance are met. Be sure to include output to support your decision on whether the assumptions have been met. (Continue with the analyses even if assumptions are not met.)Conduct two-way ANOVA with interaction and post hoc analysis (as appropriate) using Tukey to correct for multiple comparisons. Provide relevant SPSS output. Interpret the analysis results in the context of the research question. Include important statistics from your analysis results to support your conclusion and generalize your results, if appropriate, to the relevant population(s). Conduct a multiple linear regression using SPSS. Provide relevant SPSS output and assess the statistical significance of the effect of sex, age, and BMI on systolic blood pressure.Explain the assumptions of Linearity, Sampling independence, Normality, and Homoscedasticity (or equal variance). How would you test whether these have been met? (Note: for the exam you do not need to test these assumptions) Explain the practical implications of your finding. Include a reference to the R square of the model in your discussion. Discuss whether or not there is interaction (effect modification) between sex and age. Conduct simple logistic regression of coronary heart disease and sex. Conduct a multiple logistic regression using SPSS to address the research question: What is the association between sex and coronary heart disease after controlling for age and BMI?Discuss how the addition of age and BMI in the model affected the association of sex and coronary heart disease using the Odds Ratios and confidence intervals in your output. Assess the statistical significance of the individual risk factors and explain the practical implication of your finding. Complete a Kaplan-Meier Survival Analysis using Followup as the Time variable, Chdfate as the status variable and Sex as the factor. Produce a plot of the survival function. Discuss whether the survival time appears related to whether the person is male or female based on the survival plot. Use Kaplan-Meier in SPSS to test the assumption of proportionality. Create a Hazard plot with time = followed, status=Chdfate, and factor = sex. Interpret the results.Conduct a Cox Proportional Hazard regression to compare the time to coronary heart disease event between men and women. Include a Plot of the Hazards function stratified by sex in the output. Interpret the results. How does the hazard ratio compare to the odds ratio obtained from the simple logistic regression from the previous problem? Why might they differ?

 Use the pie chart, which shows the number of Congressional Medal of Honor recipients, to find the probability that a randomly chosen recipient served in the Army, Navy, or Marines