Question

question 1 (1 point)
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 between -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
i and iv
i and ii
iii and iv
question 2 (5 points)
a county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called east meadow. one of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. consequently, the appraiser decided to fit the simple linear regression model, ( widehat{y}=\beta_{0}+\beta_{1}x ), where y = appraised value of the house (in $thousands) and x = number of rooms. using data collected for a sample of n = 74 houses in east meadow, the following results were obtained:
y = 74.80 + 19.83x
s = 71.24, t = 1.05 (for testing 70) = 71.24 t = 1.05 (for testing 70)

Explanation:

• Statement I: A linear correlation coefficient of zero means no linear relationship, but there could be a non - linear relationship. So, this statement is false.
• Statement II: The sign of the slope of the regression line ($\beta_1$) and the linear correlation coefficient ($r$) is the same. If the slope is negative, the correlation coefficient is negative. This statement is true.
• Statement III: By definition, the value of the linear correlation coefficient $r$ always lies between $- 1$ and $1$ ($-1\leq r\leq1$). This statement is true.
• Statement IV: The magnitude of the correlation coefficient determines the strength of the linear relationship. $|r| = 0.82$ (for $r=-0.82$) is greater than $|r|=0.62$ (for $r = 0.62$). So, $r=-0.82$ suggests a stronger linear relationship. This statement is false.

Answer:

II and III