I have this much done, but need help with E, i,ii,iii Which asks: Choose a year other than the one from part 2c. A birth year or the first year might be a good choice(I picked 1990) .i. Use the trend line equation to estimate the y-value for the year of your choice. Find the relative change in the y-value for your chosen year compared to the last year’s value you found in part 2c iii. Interpret the meaning of your relative change value. F.Should we use the trend line model to estimate the y-value for 2020? Why or why not? Note: Hey there! Thank you for the question. As you have posted multiple sub-parts, we have helped you solve the first three parts, according to our policy. Please re-post the other parts with complete background information. Step 2 Calculation: As it is required to build a scatterplot with a trendline, we need to use Excel, where this feature is available. The independent or predictor variable is year, which we have denoted as x, and the dependent or response variable is discards, which we have denoted as y. We have entered the data in Excel as follows: Select the two columns of the data including the labels > Insert > Insert (X, Y) or Bubble Chart > Scatter. Go to Design > Quick Layout, and select a layout which displays the chart title, and both axes titles. Right click on the graph on any of the plotted points, and select the option Add Trendline from the list. From Trendline Options, select Linear, and tick on the boxes for Display Equation on chart, and Display R-squared on chart. The following output is obtained: Observe that the points lie quite close to the fitted linear trendline, without deviating too much from it. Further, there is a general increasing trend, where higher values of y are associated with higher values of x in general. This indicates a strong positive (as the slope is increasing) linear relation between x and y, and suggests that the correlation between them would be strong, as the correlation measures the strength of the linear relationship between two variables. This can be verified by finding the actual correlation coefficient. In an empty cell, type the formula: =CORREL(A2:A24,B2:B24) and press Enter. The correlation coefficient is approximately 0.965325, which is positive and very close to 1. Cleary, it is verified that a very strong positive linear relationship exists between x and y, and the correlation is strong. From the graph, the equation of the fitted trendline is: ŷ = –2562.4 + 1.3043 x. Recall that x denotes the year, and ŷ is the predicted discards. b. In a simple regression model, the coefficient corresponding to the predictor, say x, gives the amount of change in the value of the response variable for unit increase in x. If the coefficient is positive, then it means that the response variable increases with an increase in x, whereas if the coefficient is negative, then it means that the response variable decreases with an increase in x. Here, the slope is 1.3043, which is positive. Thus, for every 1-year increase in time, there is an average increase in discards by 1.3143 billion in lbs. c. The last available year in the data set is 2012. To estimate the value for this year, substitute x = 2012 in the equation. ŷ = –2562.4 + 1.3043 x = –2562.4 + (1.3043 × 2012) = –2562.4 + 2624.2516 = 61.8516. Thus, the estimated value for the last available year, 2012 is, 61.8516 billion in lbs. d. The actual value for the year 2012 in the data set is, y = 58. The estimated value is, ŷ = 61.8516. Now, y – ŷ = 58 – 61.8516 = –3.8516. As y < ŷ, the model slightly overestimates the value for 2012.
I have this much done, but need help with E, i,ii,iii Which asks:
- Choose a year other than the one from part 2c. A birth year or the first year might be a good choice(I picked 1990)
.i. Use the trend line equation to estimate the y-value for the year of your choice.
- Find the relative change in the y-value for your chosen year compared to the last year’s value you found in part 2c
iii. Interpret the meaning of your relative change value.
F.Should we use the trend line model to estimate the y-value for 2020? Why or why not?
Note:
Hey there! Thank you for the question. As you have posted multiple sub-parts, we have helped you solve the first three parts, according to our policy. Please re-post the other parts with complete background information.
Calculation:
As it is required to build a
The independent or predictor variable is year, which we have denoted as x, and the dependent or response variable is discards, which we have denoted as y.
We have entered the data in Excel as follows:
Select the two columns of the data including the labels > Insert > Insert (X, Y) or Bubble Chart > Scatter.
Go to Design > Quick Layout, and select a layout which displays the chart title, and both axes titles.
Right click on the graph on any of the plotted points, and select the option Add Trendline from the list.
From Trendline Options, select Linear, and tick on the boxes for Display Equation on chart, and Display R-squared on chart.
The following output is obtained:
Observe that the points lie quite close to the fitted linear trendline, without deviating too much from it. Further, there is a general increasing trend, where higher values of y are associated with higher values of x in general.
This indicates a strong positive (as the slope is increasing) linear relation between x and y, and suggests that the
This can be verified by finding the actual
In an empty cell, type the formula: =CORREL(A2:A24,B2:B24) and press Enter. The correlation coefficient is approximately 0.965325, which is positive and very close to 1. Cleary, it is verified that a very strong positive linear relationship exists between x and y, and the correlation is strong.
From the graph, the equation of the fitted trendline is:
ŷ = –2562.4 + 1.3043 x.
Recall that x denotes the year, and ŷ is the predicted discards.
b.
In a simple regression model, the coefficient corresponding to the predictor, say x, gives the amount of change in the value of the response variable for unit increase in x. If the coefficient is positive, then it means that the response variable increases with an increase in x, whereas if the coefficient is negative, then it means that the response variable decreases with an increase in x.
Here, the slope is 1.3043, which is positive.
Thus, for every 1-year increase in time, there is an average increase in discards by 1.3143 billion in lbs.
c.
The last available year in the data set is 2012. To estimate the value for this year, substitute x = 2012 in the equation.
ŷ
= –2562.4 + 1.3043 x
= –2562.4 + (1.3043 × 2012)
= –2562.4 + 2624.2516
= 61.8516.
Thus, the estimated value for the last available year, 2012 is, 61.8516 billion in lbs.
d.
The actual value for the year 2012 in the data set is, y = 58.
The estimated value is, ŷ = 61.8516.
Now, y – ŷ = 58 – 61.8516 = –3.8516.
As y < ŷ, the model slightly overestimates the value for 2012.
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