# What is the equation of the least-squares regression line?

DailyCalories is the explanatory variable, and WeightChange is the response variable. Create a scatterplot of the data in SPSS. Describe the form, direction, and strength of the relationship. Identify any outliers on your graph.

2. Add the least squares regression line to the scatterplot from #1. Add this graph to your output.

3. What is the correlation between the two variables? Include the output which contains the Pearson’s correlation and the state the value below.

4. Run the regression in SPSS. Include a copy of the model summary table and the coefficients table in your output.

5. What percent of variation in WeightChange is 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. (What do we like this value to be?)

6. 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.

7. Calculate (by hand, showing your work) the predicted WeightChange when the DailyCalories is 2600.

8. Calculate (by hand, showing your work) the residual for the 20 year old male in the dataset with DailyCalories of 2600. (Hint: see calculations for the previous problem and Subject 62 in the data.)

9. Use SPSS to calculate a 95% individual prediction interval for the WeightChange of the 20 year old male subject above. Refer to pages 13 and 14 in the SPSS Instruction Manual.

10. Make a Normal probability plot of the residuals. Attach the graph as part of your work.

• Do the points fall around the 45 degree line? (Yes or No)

• Does the distribution of the residuals look Normal? (Yes or No)

11. 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. Attach the graph as part of your work. Refer to page 22 in the SPSS Instruction Manual.

• Do the residuals fall randomly around the 0 reference line? (Yes or No)

• Is the assumption of linearity met? (Yes or No)

• Can you find any clear pattern in the residual plot? (Yes or No)

• Is the assumption of constant variance met? (Yes or No)

•Please circle any outliers in the residual plot, and identify the corresponding subject(s) in the dataset by their gender, age, and subject id. If there are no outliers, explain why.