MAT 120 Regression Assignment

MAT/120 REGRESSION ASSIGNMENT

Exercises.

(1) Table 2 contains price-supply data and price-demand data for soybeans.

• Enter the data into a spreadsheet.

• Create the scatter plots for the price-supply, where x is the supply (in billions of bushels) and y is the price (in dollars). Do the same for price-demand.

• Adjust the minimum and maximum of the axes of each plot to slightly below and slightly above the data values.

• Compute the regression equations for supply and for demand using linear re-gression on each of the plots. The trendline will be y = ax + b for some values of a and b. Round a and b to 3 decimal places.

• Use the trendlines to find the equilibrium price for soybeans. (Hint: The supply model will be an increasing linear function. The price model will be a decreasing linear function. Set the two equations equal to each other and solve for the equilibrium value x, and then find the corresponding value for y equilibrium price.)

Table 2. Supply and demand for soybeans.

Demand (billion bu) Price ($/bu)

 (2) Table 3 contains data for fuel consumption (mpg) of an outboard motor at various rpm.

• Enter the data into a spreadsheet so that x represents the rpm in thousands.

e.g. enter x = 1.5 for 1500, enter x = 2.0 for 2000 etc.

• Create the scatter plot for the fuel consumption y (mpg) as a function of engine speed x (rpm).

• Adjust the minimum and maximum of the axes of each plot to slightly below and slightly above the data values.

• Compute the regression equation using quadratic (polynomial order 2) regres-sion. The trendline will be y = ax2 +bx+c for some values of a, b, and c. Round a, b, and c, to 3 decimal places.

• Use your regression equation to estimate the fuel consumption at 2100 rpm (x = 2.1).

Table 3. Fuel consumption for outboard motor.

rpm                  mpg

1500                8.4

2000                6.5

2500                4.8

3000                4.0

3500                3.7

(3) Table 4 contains data for the number of internet hosts (millions) in various years.

• Enter the data into a spreadsheet so that x represents the number of years since

1990. e.g enter x = 4 for 1994, enter x = 7 for 1997, etc.

• Create the scatter plot for the number of hosts y (millions) as a function of x

(years since 1990).

• Adjust the minimum and maximum of the axes of each plot to slightly below and slightly above the data values.

• Compute the regression equation using exponential regression. The trendline will be y = aebx for some values of a and b. Round a and b to 3 decimal places.

• Use your regression equation to estimate the number of hosts in 2018 (x = 2018 − 1990 = 28).

Table 4. Internet hosts.

Year                Hosts (millions)

1994                2.2

1997                16.0

2000                50.2

2003                149.5

2006                382.0

2009                945.1

(4) Table 5 contains data for the number of dairy cows (thousands) in the U.S. in various years.

• Enter the data into a spreadsheet so that x represents the number of years since

1940. e.g enter x = 10 for 1950, enter x = 20 for 1960, etc.

• Create the scatter plot for the number of cows y (thousands) as a function of x

(years since 1940).

• Adjust the minimum and maximum of the axes of each plot to slightly below and slightly above the data values.

• Compute the regression equation using logarithmic regression. The trendline will be y = aln(x) + b for some values of a and b. Round a and b to the nearest whole number.

• Use your regression equation to estimate the number of dairy cows in 2020 (x = 2020 − 1940 = 80).

Table 5. Dairy cows on farms in the U.S.

Year                Cows (thousands)

1950                24560

1960                17356

1970                14014

1980                11123

1990                9093

2000                7500