Linear Regression Task Instructions For Excel Practice

Linear Regression Taskinstructions For Excel Practical First Attempt

Linear Regression Task Instructions for Excel Practical: First attempt the linear regression task. Please use the data that is on the following slide, titled "Assignment Data" to complete the first part of the assignment. Then follow up with the next two tabs to perform a multiple regression using Excel. The first multiple regression example is already completed for you in the Lecture. Part 1: Complete the following Task Create a scatterplot of the data on the next tab. Be sure to label the axes and include a regression line. Be sure to include the equation and r-squared value and place it on the top right of the graph. Part 2: Interpret your results: please type in your answers to the following questions. Be sure to fully elaborate on them and try to include at least 2-3 sentences to explain each part. A. What kind of correlation (positive, negative, or no correlation) exists between the MPG of a car and its acceleration time? Is it a strong correlation? B. What are the degrees of freedom of the data set? Using the critical values table in the Lecture, is the R-squared Statistic significant enough for us to make any statistical inferences? If not, how large should the sample be to substantiate the results of this study? C. Should we interpret the y-intercept in this case? Why or why not? D. Using your equation, predict the MPG of a car that accelerates in 7.5 seconds. E. In a few sentences, summarize the findings of this study? What effect does MPG consumption have on the acceleration time of a vehicle? Linear Regression Data Acceleration MPG Data retrieved from: Honda Accord Hybrid EX 7.4 47 Toyota Camry Hybrid LE 7.8 47 Chevrolet Malibu Hybrid 8 41 Hyundai Sonata Hybrid SE 8.2 39 Ford Fusion SE Hybrid 8.3 39 Toyota Camry LE (4-cyl.) 8 32 Nissan Altima 2.5 SV 7.6 31 Honda Accord EX (1.5T) 7.7 31 Chevrolet Malibu LT (1.5T) 8.4 29 Kia Optima EX (4-cyl.) 8 28 Hyundai Sonata SEL (4-cyl.) 8.3 28 Volkswagen Passat SE (4-cyl.) 8.6 28 Mult Regression_Height Height Momheight Dadheight Outlier? Prediction Error Five Number Summary for Height Minimum: st quartile: Median: rd quartile: Maximum: Outlier Parameters IQR: Lower Limit Upper Limit # of outliers .............5 65.........5 65... Attribution: n=214 female students at University of California at Davis Please perform the multiple regression for each of these tabs and do not delete them. Please include the output of your regressions to this assignment. Mult Regression_Bodyfat Triceps Thigh Midarm Bodyfat z-score outlier? 19.5 43.1 29.1 11..7 49.8 28.2 22..7 51...8 54.3 31.1 20.1 Outlier Parameters Calculate for Bodyfat Column 19.1 42.2 30.9 12.9 IQR: mean: 25.6 53.9 23.7 21.7 Lower Limit median: 31.4 58.5 27.6 27.1 Upper Limit mode: 27.9 52.1 30.6 25.4 # of outliers standard deviation: 22.1 49.9 23.2 21.3 # of outliers 25.5 53.5 24.8 19..1 56...4 56.7 28.3 27..7 46...7 44.2 28.6 17..6 42.7 21.3 12..5 54.4 30.1 23..7 55.3 25.7 22..2 58.6 24.6 25..7 48.2 27.1 14...5 21.1 Attribution: Data source: Applied Regression Models, (4th edition), Kutner, Neter, and Nachtsheim Run a multiple regression that predicts bodyfat based on midarm, thigh, and triceps measurements. Write your equation here: Using the model, provided, find the predicted body fat of someone who has a triceps measurement of 21.4, thigh of 45.6, and midarm measurement of 27.6. Show your work below: Sheet1 Starting Weight Final Weight Weight Loss Determine for weight loss column .5 Sample Mean: .5 Null Population Mean: Sample Standard Deviation: Sample Size: Standard Error: .5 CI Lower Limit .5 CI Upper Limit Perform Hypothesis Test T-Statistic: T-critical Value(s) .5 Reject the Null Hypothesis? .........5 A company wants to (cheaply) test the effects of a weight loss drug they're developing. They claim that the drug will help any person who is overweight lose 5 pounds in a week. They decide to conduct a hypothesis test at the 99% significance level to further strengthen their claim. Thus they decide to compensate a group of 40 people who are overweight to take this drug for a week and come back for a weight in. They decided to proceed with a hypothesis test and they want to disprove the null hypothesis that their drug does not help people who are overweight with weight loss (that is, m=0) Part A: State the null hypothesis and alternative hypotheses for this particular test. Part B: Use the data given to determine the following statistical measures and find the confidence interval at 99% for the average weight loss in one week. Is a 5 pounds loss contained within this confidence interval? If so, does that mean that customers can expect to lose 5 pounds on this drug? Part C: Perform a hypothesis test! Which type of tailed-test will you use? Find the t-statistic for the data and determine whether to reject the null hypothesis. Hint: the critical value of the t-distribution with 39 degrees of freedom is approximately 2.426. If you have two critical values, separate them with commas and list your positive value first in the T-Critical Value(s) cell. Part D: Were you able to reject the null hypothesis at 99% significance? If so, interpret the significance of this rejection. Does it provide sufficient evidence to prove that their drug helps their customers lose 5 pounds in one week? If you think this is insufficient evidence, describe how you would change the experiment to make it more meaningful.

Paper For Above instruction

The task involves conducting both simple and multiple linear regression analyses using Excel, focusing on understanding relationships between variables and interpreting statistical results. The initial step is to create a scatterplot of the provided data relating to vehicle fuel efficiency and acceleration time, which involves labeling axes, adding a regression line, and annotating the equation with the R-squared value in the top right corner. This visual aid helps in grasping the nature and strength of the relationship between miles per gallon (MPG) and acceleration time. Interpreting the correlation involves assessing whether the data indicates a positive, negative, or negligible association and determining its strength based on the correlation coefficient or R-squared value.

In the subsequent analysis, the degrees of freedom for the dataset are calculated, typically as the number of observations minus the number of estimated parameters. Using the critical values table from the lecture resources, one can assess whether the R-squared value indicates statistical significance, which is crucial for making valid inferences. If the R-squared is not significant, larger sample sizes might be necessary to achieve statistical confidence.

Interpreting the y-intercept in the regression model involves evaluating whether its value makes practical or theoretical sense within the context of the data. Often, if the independent variable cannot naturally be zero, the intercept lacks meaningful interpretation. Using the regression equation, a prediction can be made—for example, estimating the MPG of a car that accelerates in 7.5 seconds—by substituting the value into the regression equation. This demonstrates the model's utility in forecasting outcomes based on known predictors.

The analysis extends to summarizing the key findings, emphasizing how variables like MPG and acceleration time are related. Typically, a negative correlation suggests that higher fuel efficiency (greater MPG) corresponds to shorter acceleration times, indicating a more performant vehicle. The strength of this relationship, derived from the correlation coefficient or R-squared, indicates how well the independent variable explains the variation in the dependent variable.

Beyond the vehicle data, the task includes performing multiple regression analyses on datasets related to health and physical measurements, such as predicting body fat from anthropometric measures. The regression equation derived from this analysis allows prediction of body fat percentage based on thigh, triceps, and midarm measurements. For instance, inputs like triceps measurement of 21.4, thigh of 45.6, and midarm of 27.6 can be plugged into the model to estimate body fat percentage, illustrating its practical application.

Additionally, hypothesis testing is conducted to evaluate claims about weight loss drugs. The null hypothesis typically states no effect (e.g., no weight loss), against the alternative that the drug helps reduce weight by at least 5 pounds. Calculating confidence intervals at a 99% level with a sample size of 40 and degrees of freedom 39 allows inspection of whether the targeted weight loss amount is plausible within the interval. The t-statistic assesses whether observed data significantly deviates from the null hypothesis. If the null is rejected, it indicates sufficient evidence supporting the drug's efficacy; if not, it suggests more rigorous or larger samples are needed for conclusive results.

This comprehensive analysis underscores the importance of regression models and hypothesis tests in real-world research, emphasizing their role in making informed decisions based on statistical evidence. Accurate interpretation of these results ensures valid conclusions about variable relationships and treatment effects, ultimately contributing to improved decision-making in fields such as automotive engineering and health sciences.

References

• Kutner, M. H., Neter, J., & Nachtsheim, C. J. (2004). Applied Regression Models (4th ed.). McGraw-Hill/Irwin.
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