Hi I just need help with the boxes that need to be filled in, I dont understand
ID: 2947434 • Letter: H
Question
Hi I just need help with the boxes that need to be filled in, I dont understand how to find the answer, thank you.
Some types of algae have the potential to cause damage to river ecosystems. Suppose the accompanying data on algae colony density (y) and rock surface area (x) for nine rivers is a subset of data that appeared in a scatterplot in a research paper in a scientific journal. x 50 55 50 79 44 37 70 45 49 y 152 48 22 35 33 176 13 185 25 (a) Compute the equation of the least-squares regression line. (Round your numerical values to five decimal places.) (b) What is the value of 2 for this data set? (Round your answer to three decimal places.) Write a sentence interpreting the value of r2 in context. O This value represents the proportion of variation in rock surface area that cannot be attributed to the approximate linear relationship between rock surface area and algae colony density. This value represents the proportion of variation in algae colony density that can be attributed to the approximate linear relationship between rock surface area and algae colony density. colony density. density. O This value represents the proportion of variation in algae colony density that cannot be attributed to the approximate linear relationship between rock surface area and algae O This value represents the proportion of variation in rock surface area that can be attributed to the approximate linear relationship between rock surface area and algae colony (c) What is the value of se for this data set? (Round your answer to two decimal places.) Write a sentence interpreting the value of so in context O Observed algae colony density values tend to be s, below the values predicted by the least-squares regression line on average All observed algae colony density values are exactly se from the values predicted by the least-squares regression line. O All observed rock surface area values are exactly se from the values predicted by the least-squares regression line.Explanation / Answer
Following is the R-Code
> df <- data.frame(x=c(50,55,50,79,44,37,70,45,49),y=c(152,48,22,35,33,76,13,185,25))
> df
x y
1 50 152
2 55 48
3 50 22
4 79 35
5 44 33
6 37 76
7 70 13
8 45 185
9 49 25
> model.lm <- lm(y~.,data=df)
> model.lm
Call:
lm(formula = y ~ ., data = df)
Coefficients:
(Intercept) x
160.960 -1.795
> predict(model.lm)
1 2 3 4 5 6 7 8
71.22720 62.25396 71.22720 19.18239 81.99509 94.55763 35.33423 80.20044
9
73.02185
Our model is:
Y = 160.960 -1.795 X
> summary(model.lm)
Call:
lm(formula = y ~ ., data = df)
Residuals:
Min 1Q Median 3Q Max
-49.23 -48.02 -18.56 15.82 104.80
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 160.960 88.818 1.812 0.113
x -1.795 1.625 -1.105 0.306
Residual standard error: 60.87 on 7 degrees of freedom
Multiple R-squared: 0.1484, Adjusted R-squared: 0.02678
F-statistic: 1.22 on 1 and 7 DF, p-value: 0.3058
R2 = 0.1484
(b) This value represents the proportion of variation in algae colony density(y) that can be attributed to the approximate relationship between x & y.
Se = 60.87
Observed algae colony density values tend to deviate from the value predicted by the least square regression line by Se on an average
> cor(df$x,df$y)
[1] -0.3852747
r= -0.3852747
negative and moderate