Simple Linear Regression Report

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Simple Linear Regression Report

Description

Use the dependent variable (labeled Y) and one of the independent variables (labeled X1, X2, and X3) in the data file. Select and use one independent variable throughout this analysis. Use Excel to perform the regression and correlation analysis to answer the following. The week 6 spreadsheet can be helpful in this work.

  • Generate a scatterplot for the specified dependent variable (Y) and the selected independent variable (X), including the graph of the "best fit" line. Interpret.
  • Determine the equation of the "best fit" line, which describes the relationship between the dependent variable and the selected independent variable.
  • Determine the correlation coefficient. Interpret.
  • Determine the coefficient of determination. Interpret.
  • Test the utility of this regression model by completing a hypothesis test of b=0 using ?=0.10. Interpret results, including the p-value.
  • Based on the findings in steps 1-5, analyze the ability of the independent variable to predict the dependent variable.
  • Compute the confidence interval for b, using a 95% confidence level. Interpret this interval.
  • Compute the 99% confidence interval for the dependent variable, for a selected value of the independent variable. Each student can choose a value to use for the independent variable (use same value in the next step). Interpret this interval.
  • Using the same chosen value for part (8), estimate the 99% prediction interval for the dependent variable. Interpret this interval.
  • What can be said about the value of the dependent variable for values of the independent variable that are outside the range of the sample values? Explain.
  • Describe a business decision that could be made based on the results of this analysis. In other words, how might the business operations change based on these statistical results.

Explanation & Answer length: 3 pages.

Project Part B: Hypothesis Testing By 1 Contents 1. Introduction ............................................................................................................................. 3 2. Hypothesis Test 1: Mean Sales per Week ............................................................................... 4 3. Hypothesis Test 2: Proportion receiving online training ......................................................... 5 4. Hypothesis Test 3: Mean calls made among those with no training ....................................... 6 5. Hypothesis Test 4: The mean time per call ............................................................................. 7 6. Summary.................................................................................................................................. 8 7. References ............................................................................................................................... 9 2 1. Introduction Hypothesis testing is a kind of a tool in statistics by which we can test an assumption which is related to the population parameter. This report consists of ‘Hypothesis test’ practice sections, which is a very useful tool for testing claims made by various people or organizations as well as in research studies. The test performed here are real life examples of how this testing can be used to come to a conclusion about any claims.

The test has been performed in a very orderly manner in this report. At first, a claim statement has been made (given in question). After that, we have made a null and alternative hypothesis, which is followed by calculation of required statistics and then finally rejecting or failing to reject the null hypothesis. 3 2. Hypothesis Test 1: Mean Sales per Week Hypothesis statement The mean sales per week exceeds 42.5 per salesperson. Null and alternate hypotheses Hₒ: μ=42.5 Ha: μ>42.5 Type of test Right tail test because the hypothesis contains > symbol. Use z or t? Select t test because we have sample standard deviation. Rejection region Assume α = 0.05. Rejection region t>1.6604 Test statistic 4.856 p-value 0.000002 Hypothesis test result using p-value We reject the null hypothesis as p value is less than α. Hypothesis test result using test statistic We reject the null hypothesis as test statistic > 1.6604. Do the results support the claim being made?

Since we are rejecting Hₒ, we have support for Ha, which is manager’s belief. So, we can say the result provide the evidence to support the manager’s belief, i.e. we can say that the mean sales per week exceeds 42.5 per sales person. 99% Confidence Interval for the mean You can be 99% confident that the population mean falls between 43.59 and 46.15. 4 3. Hypothesis Test 2: Proportion receiving online training Hypothesis statement The proportion receiving online training is less than 55%. Null and alternate hypotheses Hₒ: p=55% Ha: p

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