Scatter Plot Correlation AP Stat Review

In a statistics course, a linear regression equation was computed to predict the final exam score based on the score on the first test of the term. The equation was y=25+0.7x where y is the final exam score and x is the score on the first test. George scored 80 on the first test. On the final exam George scored 85. What is the value of his residual?

• -4

• 4

• 4.5

• 5

• 81

Which of the following best describes the correlation between two variables if r = 0.987?

• positive and strong

• negative and weak

• positive and weak

• negative and strong

• no correlation

Tags

CCSS.HSS.ID.C.8

The correlation coefficient is

• always equal to the slope of the regression line

• a positive number that measures the goodness of fit

• never equal to zero

• A number between -1 and +1 that measures the strength and direction of the linear relationship between two variables

• the fraction of the variation in the values of y that is explained by the least-squares regression of y on x.

Tags

CCSS.HSS.ID.C.8

The equation of the least squares regression line for a set of points in a scatterplot is given above. The point (5, 7) is one point on this scatterplot. Which of the following is the residual for the point (5, 7)?

• 6.25

• 4.05

• 0.71

• 0.75

• 7.87

Consider the following scatterplots above. What is the relationship between r₁, r₂, and r₃, the correlation coefficients of each scatterplot?

• r₂ < r₁ < r₃

• r₁ < r₂ < r₃

• r₁ < r₃ < r₂

• r₂ < r₃ < r₁

• r₃ < r₂ < r₁

Tags

CCSS.HSS.ID.B.6

CCSS.HSS.ID.C.8

For the years 1950-1980, the number of heart disease deaths per 100,000 people in the United States were recorded. The regression line below was computed using a statistical software package. which statement is the correct interpretation of the slope?

The regression equation is

Number of deaths = 7387 - 3.63 year

• Heart disease will be cured in the year 2036.

• The regression line estimates that for every 3.63 years there is an average of 1 death due to heart disease per 100,000 people.

• For every 3.63 years there is a decrease on the average of 1 death due to heart disease per 100,000 people.

• There is an increase of approximately 7387 deaths per year.

• The number of heart disease deaths per 100,000 people has been dropping by an estimated 3.63 deaths per year on the average.

Tags

CCSS.HSS.ID.C.7

A researcher wishes to examine the relationship between years of schooling completed and the number of pregnancies in young women. Her research discovers a linear relationship, and a least squares fit for her data results in the model above, where x is the number of years completed in school and y is the number of pregnancies. What is the estimated change in the number of pregnancies that corresponds to the completion of an additional 10 years of school?

• a decrease of 1.2

• a decrease of 5.2

• an increase of 7.6

• a decrease of 7.6

• an increase of 1.2

Tags

CCSS.HSA.CED.A.2

CCSS.HSS.ID.C.7

A linear model was constructed for a set of bivariate data using least squares regression techniques. Given the residual plot shown, what conclusion should be drawn?

• A linear model was not a good fit for the data.

• A linear model was a good fit for the data.

• The correlation between the original variables is close to 1.

• The data was drawn from a population that was not normally distributed.

• The study was poorly designed.

Residuals are

• possible models not explored by the researcher.

• the difference between the observed response and the values predicted by the model.

• variation in the response variable that is explained by the model.

• data collected from individuals that is not consistent with the rest of the group.

• a measure of the strength of the linear relationship between x and y.

A study is conducted to determine if one can predict the yield of a crop based on the amount of fertilizer applied to the soil. 
The response variable in this study is...

• yield of the crop.
• amount of fertilizer applied to the soil.
• the experimenter.
• the soil.