From 2010–2020, the correlation coefficient between students’ performance on the NJ graduation exams and the NJ graduation rate is 0.885. Based on this information, which of the following statements are true?

A botanist collected data on growth patterns for a given plant over 5 weeks and a least squares regression line was fitted to the data. The resulting equation was $ŷ = 3 + 0.25x$ where $x$ is the number of weeks and $y$ is the height of the plant in centimeters. What can be concluded from this equation?

I.    The plant was 0.25 cm tall when first measured.

II.   The plant grew at an average rate of 0.25 cm per week.

III.  The plant grew at an average rate of 3 cm per week.

IV.  In 3 more weeks, given the same growth rate, the plant will be approximately 5 cm tall.

V.  In 3 more weeks, given the same growth rate, the plant will be approximately 3.75 cm tall.

Which of the following residual plots indicates a linear association between the variables?

What can we say about the correlation for that data shown in the scatter plot?

I.    Positive correlation

II.   Negative correlation

III.  Strong correlation

IV.  Moderate correlation

V.  Weak correlation

A student created a least squares regression line, then calculated residuals to determine if it was the most appropriate line for the data. The student got the residual plot shown. What is true about the least squares regression line?

The following table shows the data collected from a group of boys and girls about their favorite beverage.

Which of the following statements is supported by the table?

The following data were collected from a random sample of people, who identified their favorite animal. The results are shown in the following two-way table.

Which of the following statements are true based on the information in the two way table?

I.    The proportion of men who identified bird as their favorite animal is 50/500.

II.   The proportion of women who identified cat as their favorite animal is 200/1000.

III.  The proportion of people who identified dog as their favorite animal is 450/1000.

The equation $y = 2.579 + 0.99x$ represents the least squares regression line that summarizes the relationship between the height ($y$) in centimeters of a certain plant in respect to time ($x$) in days recorded by a scientist over the past month. What does the scientist predict the height of the plant will be after 10 days?

A data analyst collected data to predict monthly subscribers to a youtube channel from monthly social media posts. The model created from the data showed that 49 percent of the variation in monthly subscribers could be explained by monthly social media posts. What is the value of the correlation coefficient?

In a set of data, an exponential relationship exists between the response and explanatory variables. After taking the common logarithm of each response variable value, the equation of the least-squares regression line is $\log(y) = 4.6 – 1.2x$.

Which of the following numbers represents the predicted value of the response variable for $x$ = 2.9.