Unit 2 Review

The table below shows the data on hours students (A - E) spent studying and exam scores.

Write the linear regression equation, rounding to the nearest hundredth. Write what does x and y represent using context.

Answer explanation

y = 4.01x + 60.12 where y represents the exam score and x represents the hours studied.

Tags

CCSS.HSF.LE.B.5

The table below shows the data on hours students (A - E) spent studying and exam scores.

State the correlation coefficient, rounded to the nearest hundredth.

Answer explanation

Correlation Coefficient: r = 1.00

The table below shows the data on hours students (A - E) spent studying and exam scores.

Interpret the value of r in the context of this data set.

Answer explanation

The correlation coefficient when rounded becomes 1.00 indicating a perfect positive linear relationship between the number of hours studied and the exam scores.

This means that as the number of hours studied increases, the exam score increases perfectly consistently and predictably.

The data in the table below show some of the results of a study comparing the height of a certain breed of dog, based on its mass.

Write the linear regression equation for these data, where x is the mass and y is the height.

Round all values to the nearest tenth.

Answer explanation

y =1.9x +29.8  

The data in the table below show some of the results of a study comparing the height of a certain breed of dog, based on its mass.

State the value of the correlation coefficient to the nearest tenth, and explain what it indicates.

Answer explanation

 r = 0.3

This indicates a weak relationship between a dog’s height and mass.

A company that produces scarves tracks the number of scarves sold for each style-color combination and their average sale price. They create a scatter plot with the number of scarves sold on the x-axis and the average price per scarf (in dollars) on the y-axis. The data suggests a linear relationship. Which equation best represents the line of best fit?

• y = -225x + 1,124

• y = -0.004x + 5

• y = -x + 5

• y = 0.01x + 5

Answer explanation

The slope (−0.004) indicates a very slight decrease in the average price as the number of scarves increases, which aligns with expectations in real-world pricing scenarios where discounts might occur with larger orders.

A survey of 150 students was taken. It was determined that ⅔ of the students play video games. Of the students that play video games, 85 also use social media. Of the students that do not play video games, 20% do not use social media.

Complete the two-way frequency table.

Alex collects data on the number of books in a school library and the average reading scores of students at those schools.

Alex states: "The scatter plot between the number of books in the school library and the average reading scores of students shows a strong and positive correlation. This means that adding more books to a school library directly causes students to achieve higher reading scores."

What does it mean for the relationship between the variables when the correlation is strong in this situation?

Answer explanation

A strong correlation between the number of books in the school library and average reading scores means that the data points in the scatter plot follow a clear and consistent pattern.

Specifically, schools with more books in their library tend to have higher average reading scores, and this pattern is very predictable. However, a strong correlation does not prove that one variable directly causes the other to change.

Alex collects data on the number of books in a school library and the average reading scores of students at those schools.

Alex states: "The scatter plot between the number of books in the school library and the average reading scores of students shows a strong and positive correlation. This means that adding more books to a school library directly causes students to achieve higher reading scores."

What is wrong with the last sentence of Alex's statement? Explain your reasoning.

Tags

CCSS.RI.8.7

CCSS.RI.9-10.7

CCSS.RL.7.7

CCSS.RL.8.7

CCSS.RL.9-10.7

The scatter plot compares the number of popcorn bags and the number of sodas sold at each performance of the circus over one week.

Which conclusion can be drawn from the scatter plot?

• There is a negative correlation between popcorn sales and soda sales.

• There is a positive correlation between popcorn sales and soda sales.

• There is no correlation between popcorn sales and soda sales.

• Buying popcorn causes people to buy soda.