To complete the assignment, electronically submit 2 files: Your written answers to the questions and a spreadsheet file that computes the necessary quantities to answer the questions. Consider the following data on y and x.
1. Make a scatter plot of the data in Excel or Google Sheets. Add gridlines to your graph.
2. Copy & paste your scatter plot into Paint or a similar program. Draw a line that you think Use your eye to find a line that best fits this data. Draw this line on your scatter plot using the line drawing tool. What estimates of b_0 and b_1 correspond to your line? (you can find approximate values using the gridlines on your graph to your advantage).
3. Define y┴~_i as the value of y that your eyeball model predicts for observation i (where i ranges from 1-n). In your spreadsheet, compute y┴~ and (y_i-y┴~_i )^2 for each observation. Use these to compute ∑_(i=1)^n e┴~_i^2=∑_(i=1)^n(y_i-y┴~_i )^2 (Ignore the two doted boxes in the equation).
4. Use your spreadsheet for each observation, compute (x-¯x)(y-¯y) and (x-¯x )^2. Use them to compute the least squares estimates of b_0 and b_1.
5. Use these estimates to find predicted value of y for each of the x values. Letting y┴^_i be the least squares estimate of y corresponding to an x value of x_i , compute the value of (y_i-y┴^_i )^2 for each of the 15 observations in the data. Use these computed values of (y_i-y┴^_i )^2 to compute ∑_(i=1)^n e_i^2=∑_(i=1)^n(y_i-y┴^_i )^2. (Ignore the doted boxes)
6. Compare the values ∑_(i=1)^n e┴^_i^2 and ∑_(i=1)^n e┴~_i^2. Which value is lower? Provide a justification for this finding.
7. Provide an intuitive explanation of the total sum of squares, the explained sum of squares and the unexplained sum of squares due to error.
