Stat Exam

Analysis of the data from 25 mothers indicates that an​ infant's birth weight​ (g), y​, can be estimated by a​ mother's weight​ (kg), x​, using the regression equation y =31x+1501. For every​ ________ kg increase in a​ mother's weight, the​ infant's birth weight increases by​ ________ g.

1;31

What is a​ residual?

A residual is a value of y- y with caret​, which is the difference between an observed value of y and a predicted value of y.

What is a scatterplot and how does it help​ us?

A scatterplot is a graph of paired​ (x, y) quantitative data. It provides a visual image of the data plotted as​ points, which helps to see patterns in the data.

Smoking and the episodes of lung cancer have a high​ correlation, but it does not prove​ ________.

Causation

Which of the following statements concerning the linear correlation coefficient are​ true? ​I: If the linear correlation coefficient for two variables is​ zero, then there is no relationship between the variables. ​II: If the slope of the regression line is​ negative, then the linear correlation coefficient is negative. ​III: The value of the linear correlation coefficient always lies −1 and 1. ​IV: A linear correlation coefficient of 0.62 suggests a stronger linear relationship than a linear correlation coefficient of −0.82.

II and III

Which of the following is NOT a requirement in determining whether there is a linear correlation between two​ variables?

If r>​1, then there is a positive linear correlation.

If we find that there is a linear correlation between the concentration of carbon dioxide in our atmosphere and the global​ temperature, does that indicate that changes in the concentration of carbon dioxide cause changes in the global​ temperature?

No. The presence of a linear correlation between two variables does not imply that one of the variables is the cause of the other variable.

b. In what sense is the regression line the straight line that​ "best" fits the points in a​ scatterplot?

The regression line has the property that the sum of squares of the residuals is the lowest possible sum.

In this section we use r to denote the value of the linear correlation coefficient. Why do we refer to this correlation coefficient as being​ linear?

The term linear refers to a straight​ line, and r measures how well a scatterplot fits a​ straight-line pattern.

What is the relationship between the linear correlation coefficient r and the slope b1 of a regression​ line?

The value of r will always have the same sign as the value of b1

A​ __________ exists between two variables when the values of one variable are somehow associated with the values of the other variable.

correlation

Which of the following is not equivalent to the other​ three? Independent variable Predictor variable Dependent variable Explanatory variable

dependent

A straight line satisfies the​ __________________ if the sum of the squares of the residuals is the smallest sum possible.

least squares property

The​ ______________ measures the strength of the linear correlation between the paired quantitative​ x- and​ y-values in a sample.

linear correlation coefficient

In a​ scatterplot, a(n)​ ______________ is a point lying far away from the other data points.

outlier

​A(n) ________ is a point lying far away from other data points on a scatterplot.

outlier

Given a collection of paired sample​ data, the y=b0+b1x algebraically describes the relationship between the two​ variables, x and y.

regression equation

When determining whether there is a correlation between two​ variables, one should use a​ ____________ to explore the data visually.

scatterplot

Twenty different statistics students are randomly selected. For each of​ them, their body temperature ​(degrees°​C) is measured and their head circumference​ (cm) is measured. If it is found that r=​0, does that indicate that there is no association between these two​ variables?

​No, because while there is no linear​ correlation, there may be a relationship that is not linear.

The linear​ ________ coefficient denoted by r measures the​ ________ of the linear association between two variables.

​Overall, there is no noticeable relationship between NO and CO.

The two key parts of a regression equation involve the​ ________ and the ​y-​________.

​slope; intercept