1. The accompanying table shows the number of movie theaters showing a popular film and the film's weekly gross earnings, in millions of dollars. Use the table to answer the questions 1), 2).
Number of Theaters (x)
443
456
493
530
569
657
723
1,054
Gross Earnings (y)
(millions of dollars)
2.57
2.65
3.73
4.05
4.76
4.79
5.15
9.63

1). Write the linear regression equation for this set of data, rounding values to five decimal places. Using this linear regression equation, find the approximate gross earnings, in millions of dollars, generated by 610 theaters. Round your answer to two decimal places.
2). Find the minimum number of theaters that would generate at least 7.65 million dollars in gross earnings in one week.

2. A real estate agent plans to compare the price of a cottage, y, in a town on the seashore to the number of blocks, x, the cottage is from the beach. The accompanying table shoes a random sample of sales and location data. Write a linear regression equation that relates the price of a cottage to it's distance from the beach. Use the equation to predict the price of a cottage, to the nearest dollar, located three blocks from the beach.
Number of Blocks
from the Beach
(x) Price of a Cottage
(y)
5 $132,000
0 $310,000
4 $204,000
2 $238,000
1 $275,000
7 $60,800

3. The table below represents a chart kept by a pediatrician tracking the circumference of babies heads at various months of age.
Age
(in months) Circumference
(in cm)
1 35.8
2 36.6
5 38.5
6 39.1
4 38.9
13 40.1
7 39.1
15 40.3
10 39.9
2 36.8
18 40.6

1). Determine the regression model that best fits the data, rounding all values to the nearest thousandth. Then predict the size of a baby's head at 24 months old. Round your answer to the nearest tenth.
2). The pediatrician measured a newborns head and found the circumference to be 35.1cm. Can he add the pair (0, 35.1) to the data set to calculate a new regression? Justify your answer.