Stats Lsrl

Some data were collected on the weight of a male white laboratory rat for the first 25 weeks after its birth. The linear regression equation is:
Weight = 100 + 40(Time).
Which is the best description of the slope for this regression equation in context of the problem?

• The slope of the line of regression is the time since birth of the rate. It demonstrates the predicted weight of a laboratory rate after so many months since birth.

• The slope is 40 grams/week which means the mouse gains about 40 grams per week after birth.

• The slope is 40 and it means for every increase in weeks the graph will increase. 

• The slope is 40, which tells us the line increases. 

Tags

CCSS.HSF.LE.B.5

Write the linear regression equation for the data set foot length (x) and height (y).

• yhat = 28.93 + 1.155x

• height = 28.39(foot length) + 1.155

• yhat = 1.878 + 117.99x

• height = 117.99 + 1.878(foot length)

What is the correlation value?

• .209

• .457

• .13

• .361

What is the value of the correlation coefficient, r?

• 0.921

• -0.921

• 0.957

• -0.957

A fisheries biologist studying whitefish in a Canadian Lake collected data on the length (in CM) and eg production for 25 female fish. A scatter plot of her results and computer regression analysis of egg production versus fish length are given below. (Note: number of eggs is given in 1000's so 40 means 40,000 eggs)

The equation of the LSRL is.......

• eggs = -142.74 + 39.25(length)

• eggs = 39.25 - 142.74(length)

• eggs = 25.55 + 5.932(length)

• length = 25.55 + 5.392(eggs)

• length = -142.74 + 39.25(eggs)

A fisheries biologist studying whitefish in a Canadian Lake collected data on the length (in CM) and eg production for 25 female fish. A scatter plot of her results and computer regression analysis of egg production versus fish length are given below. (Note: number of eggs is given in 1000's so 40 means 40,000 eggs). Which of the following statements can be made on the basis of the computer output?

• 83.5% of the variation in egg production can be accounted for by the LSRL of egg production on fish length

• 69.7% of the variation in egg production can be accounted for by the LSRL of egg production on fish length

• 83.5% of the variation in fish length can be accounted for by the LSRL of egg production on fish length

• 69.7% of the variation in fish length can be accounted for by the LSRL of egg production on fish length

• 68.4% of the variation in fish length can be accounted for by the LSRL of egg production on fish length

The LSRL is fit to a set of data. If one of the data points has a positive residual, then.......

• the correlation between the values of the response and explanatory variables must be positive

• the point must lie above the LSRL

• the point must lie near the right edge of the scatterplot

• the point is probably an influential piont

• all of the above

A study of child development measures the age (in months) at which a child begins to talk and also the child's score on an ability test given several years later. The study asks whether the age at which a child talks helps predict the later test score. The LSRL of test score "y" on age "x" is y-hat=110 - 1.3x. According to this regression line, what happens to children who talk one month later than other children?

• Their predicted test scores go down 110 points

• Their predicted test scores go down 1.3 points

• Their predicted test scores go up 110 points

• Their predicted test scores go up 1.3 points

• Their predicted test scores are 108.7 points

A study of the effects of television measured how many hours of television each of 125 grade school children watched per week during a school year and their reading scores. The study found that children who watch more television tend to have lower reading scores than children who watch fewer hours of television. The study report says that "Hours of television watched explained 9% of the observed variation in the reading scores of the 125 subjects." The correlation between hours of TV and reading score must be

• r = 0.09

• r = -0.09

• r = 0.3

• r = -0.3

• can't tell from the information given

You are examining the relationship between x = the height of red oak trees and y = the number of acorns produced in a five year period. You calculate a correlation coefficient and a least-squares regression line of y on x. If you switched the variables (that is, let x = number of acorns and y = height of trees), which of the following would be true?

• both the correlation coefficient and the regression line would be unchanged

• the correlation coefficient would change, but the regression line would not change

• the correlation coefficient would not change, but the regression line would change

• neither the correlation coefficient nor the regression equation would change

• only the y-intercept fo the regression line would change, the slope of the line and the correlation coefficient would not change.