Lab 6:Simple Linear Regression

NOTE: SPSS outputs are necessary to show full completion of the lab. Please paste all SPSS outputs into your lab report and submit the completed reports including all requested tables and graphs via Brightspace (under the "Lab" folder) by 11:59 pm Friday. Two points will be deducted for each SPSS requested output that is not included in the submitted lab document.Also, 30% points will be deducted for late submission, up to 24 hours.

Dataset: This lab uses the dataset (SleepPatterns), located on Brightspace under Lab in the Datasets submodule. Instructions for opening the dataset in SPSS are found as follows.

• SPSS installed on a computer: Reference page 4 of the SPSS Instruction Manual
• SPSS running remotely: Reference the slide "Opening your Dataset Remotely in SPSS via Go Remote" in the document "SPSS using Citrix access guidelines" on Brightspace.

Two hundred fifty college students in Indiana participated in a study examining the associations among sleep habits, sleep quality and physical/emotional factors. Participants completed an online survey about sleep habits that included the Pittsburgh Sleep Quality Index (PSQI), the Epworth Sleepiness Scale (ESS), the Horne-Ostberg Morningness Eveningness Scale (MES), the Subjective Units of Distress Scale (SUDS), and questions about academic performance and physical health.

We are now interested in describing the relationship between height (Height) and weight (Weight). Can we predict Weight based on only Height? Refer to pages 19, 20, 21 and 22 of in the SPSS Instruction Manual for this lab.

- (2 points) Height is the explanatory variable, and Weight is the response variable. Make a scatterplot of the data in SPSS. Include this graph in your Brightspace submission. Describe the form, direction, and strength of the relationship.

- (1 point) Add the least squares regression line to the scatterplot from #1. Include this graph in your Brightspace submission. - (1 points) What is the correlation between the two variables? Include the output which contains the Pearson's correlation in your Brightspace submission and state the value below.

- (1 point) Run the regression in SPSS. Include a copy of the model summary table and the coefficients table in your Brightspace submission.

-(2 points) What percent of variation in Weightis explained by the least squares regression line?Comment on whether this number indicates a good fit or a poor fit of our model to the data.

-(2 points) What is the equation of the least-squares regression line? Be sure to identify your variables by name, not just x and y. Also, remember to put a "hat" (^) on the response variable.

-(2 points) Calculate (by hand, showing your work) the predicted Weight when Height is 69.86. Round your final answer to 2 decimal places.

-(2 points) Calculate (by hand, showing your work) the residual for the subject (ID=27) with Height_m of 69.86.

- (2 points) Use SPSS to calculate a 95% individual prediction interval for height 69.86 of the subject mentioned in the previous problem (ID=27). Refer to pages 20 and 21 in the SPSS Instruction Manual.Round your final answer to 2 decimal places.

- (2 points) Make a Normal probability plot of the residuals. Include the graph in your Brightspace submission.

• (1 point) Do the points fall aroundthe 45-degree line?(Yes or No)
• (1 point)Does the distribution of the residuals look Normal? (Yes or No)

- (3 points) Make a residual plot with a y = 0 reference line. Make sure that the explanatory variable is in the x-axis and the residual is in the y-axis. Include the graph in your Brightspace submission.

• (1 point) Do theresiduals fall randomly around the 0-reference line?(Yes or No)
• (1 point) Can you find any clear pattern in the residual plot?(Yes or No)
• (1 point) Is the assumption of constant variance met? (Yes or No)