Setup: An experiment was conducted to study the relationship between baking temperature x (in units of 10 Fahrenheit) and yield y (as a percentage) of a popular cake mix. The results were as follows: Baking Temp x Percent Yield y (10F) (percentage) 10 21.0 10 19.9 11 22.7 11 23.7 12 25.0 15 30.5 17 36.1 19 38.8 20 41.5 20 42.5 23 45.0 25 50.0 27 54.0 30 62.2 P i Xi = 250 P i P Yi = 512.9 i X2 i = 5044 P i Y 2 i = 21116.23 P i XiYi = 10316.8

Questions:

1. Fit a simple linear regression model to the data and calculate the least-squares estimates. Give the equation of your regression line in the form y = 0 + 1x.

2. Use the regression line that you found to answer the following.

(a) If the baking temperature increases by 1 unit, how much is the percent yield expected to increase / decrease?

(b) If the baking temperature increases by 10 units, how much is the percent yield expected to increase / decrease?

Setup: The attendance at a racetrack (x) and the amount that was bet (y) on n = 10 selected days are given in the following table: Attendance x Amount Bet y (hundreds) (millions of dollars) 119 2.1 130 3.2 121 2.6 120 2.2 134 3.3 133 3.9 126 2.8 125 2.7 132 3.4 128 3.5 Other statistics from our data: x = 126.8 blank y = 2.97 sx = 5.514 sy = 0.585 sxx = 273.6 syy = 3.081 sxy = 26.54 Regression Line Equation: y = 9.33 + 0.097x

3. Using the data above, calculate the residuals for each yi , i = 1, 2, . . . , 10 and provide the residual values. (3 decimals are fine.)

4. Do the residuals appear to come from a normal distribution? Use either a Q-Q Plot and/or the Shapiro-Wilk Test (using = 0.05). Provide your plot and/or the results of the test.

5. Suppose we assume that the population variance is equal to 0.36 (so 2 is known). Find a 95% confidence interval for 1.

Setup: Suppose we know the following: X = [ 1 10 1 10 1 12 1 15 1 14 ] Y = [ 2 3 2 4 3 ] = [ 0.25 0.25 ] V() = 9 [7.356 0.587 0.587 0.048 ]

6. Identify the following (only algebra required, no complicated matrix calculations):

(a) What are the x-values in the dataset?

(b) Find the equation of the regression line in the form y = 0 + 1x.

(c) Find the value of , assuming it is known.

(d) Find V( 0).

(e) Find COV 0, 1 .

(f) Find the value of sxx.