The table shows the amount of milk that Wisconsin dairy farms produced from 1940 to 1997. Use linear model to estimate milk production in 1990.
year milk produced
1940 7
1972 7
1997 8
15.1
12.5
7.5
2.5
7.5---between 7 (1972) and 8 (1997) = 7.5
Well, if we take a look at the data, it seems like the milk production in Wisconsin has been going steady at 7 units of milk from 1940 to 1972, and then it increased to 8 units in 1997. So, from a linear perspective, it seems like the milk production has been gradually increasing over the years.
To estimate the milk production in 1990, we can assume that the trend of increasing milk production continued at a similar rate. Since we don't have the exact data for 1990, let's assume that the increase was linear over the entire time period.
Using simple linear regression, we can determine the equation of the line that best fits the data. Let's do some math... *pulls out calculator*
Alright, based on my calculations, the estimated milk production in 1990 would be around 7.5 units.
Now, I must say that this is just an estimation based on the available data and the assumption of a linear trend. The actual milk production in 1990 could be slightly different, but this gives us a rough idea.
And remember, cows are pretty unpredictable creatures. They might have had a party in 1990 and produced extra milk just for fun!
To estimate milk production in 1990 using a linear model, we will first determine the slope (rate of change) of milk production over time and then use this slope to estimate the milk production in 1990.
To find the slope, we need to calculate the change in milk production divided by the change in years between two data points. Let's use the years 1940 and 1997, and the corresponding milk production amounts for those years.
Change in milk production = 8 - 7 = 1
Change in years = 1997 - 1940 = 57
Slope = Change in milk production / Change in years = 1 / 57
Now that we have the slope, we can estimate the milk production in 1990. Let's use the initial milk production value in 1940 and the corresponding year.
Initial milk production = 7
Initial year = 1940
Target year = 1990
Change in years from initial year to target year = 1990 - 1940 = 50
Estimated milk production in 1990 = Initial milk production + (Slope * Change in years) = 7 + (1/57 * 50)
Let's calculate the estimated milk production in 1990:
Estimated milk production in 1990 ≈ 7.88
Therefore, the estimated milk production in 1990 using a linear model is approximately 7.88.
To estimate the milk production in 1990 using a linear model, we can use the given data points and find the equation of a line that represents the relationship between the year and milk production.
To do this, we need to find the slope and y-intercept of the line.
Step 1: Calculate the slope (m) using the formula:
m = (change in y) / (change in x)
m = (milk produced in 1997 - milk produced in 1972) / (year of 1997 - year of 1972)
= (8 - 7) / (1997 - 1972)
= 1 / 25
= 0.04
Step 2: Use the slope (m) and one data point (x, y) to find the y-intercept (b) using the formula:
b = y - mx
Using the data point (1972, 7):
b = 7 - (0.04 * 1972)
= 7 - 78.88
= -71.88
Step 3: Now we have the equation of the line in the form of y = mx + b, where x is the year and y is the milk production:
y = 0.04x - 71.88
Step 4: Substitute the year 1990 into the equation to estimate the milk production:
y = 0.04 * 1990 - 71.88
= 79.6 - 71.88
= 7.72
Therefore, the estimated milk production in 1990 using the linear model is approximately 7.72 units.