13.3 Linear Equations

A local small business completes federal tax returns for customers. The rate for services is $32 per hour plus a $31.50 one-time charge. The total cost to a customer depends on the number of hours it takes to complete the job.

Find the equation that expresses the total cost in terms of the number of hours required to complete the job.

Svetlana tutors to make extra money for college. For each tutoring session, she charges a one-time fee of $25 plus $15 per hour of tutoring. A linear equation that expresses the total amount of money Svetlana earns for each session she tutors is y = 25 + 15x.

What are the independent and dependent variables? What is the y-intercept and what is the slope? Interpret them using complete sentences.

True or False? If False, correct it: Suppose a 95% confidence interval for the slope β of the straight line regression of Y on X is given by -3.5 < β < -0.5. Then a two-sided test of the hypothesis $H_{0} : \beta = −1$ would result in rejection of $H_{0}$ at the 1% level of significance.

True or False: It is safer to interpret correlation coefficients as measures of association rather than causation because of the possibility of spurious correlation.

We are interested in finding the linear relation between the number of widgets purchased at one time and the cost per widget. The following data has been obtained:

X: Number of widgets purchased – 1, 3, 6, 10, 15

Y: Cost per widget(in dollars) – 55, 52, 46, 32, 25

Suppose the regression line is $\overset{^}{y} = −2.5 x + 60$. We compute the average price per widget if 30 are purchased and observe which of the following?

1. $\overset{^}{y} = 15 \text{dollars}$; o…

Discuss briefly the distinction between correlation and causality.

True or False: If r is close to + or -1, we shall say there is a strong correlation, with the tacit understanding that we are referring to a linear relationship and nothing else.