91Ó°ÊÓ

The paper "The Relationship Between Cell Phone Use, Academic Performance, Anxiety, and Satisfaction with Life in College Students" (Computers in Human Behavior [2014]: \(343-350\) ) described a study of cell phone use among undergraduate college students at a large, Midwestern public university. The paper reported that the value of the correlation coefficient between \(x=\) Cell phone use (measured as total amount of time (in hours) spent using a cell phone on a typical day) and \(y=\) GPA (cumulative grade point average (GPA) determined from university records) was \(r=-0.203\) a. Interpret the given value of the correlation coefficient. Does the value of the correlation coefficient suggest that students who use a cell phone for more hours per day tend to have higher GPAs or lower GPAs? b. The study also investigated the correlation between texting (measured as the total number of texts sent and texts received per day) and GPA. The direction of the relationship between texting and GPA was the same as the direction of the relationship between cell phone use and GPA, but the relationship between texting and GPA was not as strong. Which of the following possible values for the correlation coefficient between texting and GPA could have been the one observed? \(r=-0.30 \quad r=-0.10 \quad r=0.10 \quad r=0.30\) c. The paper included the following statement: "Participants filled in two blanks- one for texts sent and one for texts received. These two texting items were nearly perfectly correlated." Do you think that the value of the correlation coefficient for texts sent and texts received was close to \(-1,\) close to \(0,\) or close to + 1 ? Explain your reasoning.

Is the following statement correct? Explain why or why not. A correlation coefficient of 0 implies that there is no relationship between two variables.

The article "That's Rich: More You Drink, More You Earn" (Calgary Herald, April 16,2002 ) reported that there was a positive correlation between alcohol consumption and income. Is it reasonable to conclude that increasing alcohol consumption will increase income? Explain why or why not.

The paper "Noncognitive Predictors of Student Athletes' Academic Performance" (Journal of College Reading and Learning [2000]: e167) summarizes a study of 200 Division I athletes. It was reported that the correlation coefficient for college grade point average (GPA) and a measure of academic self-worth was \(r=0.48\). Also reported were the correlation coefficient for college GPA and high school GPA \((r=0.46)\) and the correlation coefficient for college GPA and a measure of tendency to procrastinate \((r=-0.36) .\) Write a few sentences summarizing what these correlation coefficients tell you about GPA for the 200 athletes in the sample.

For each of the following pairs of variables, indicate whether you would expect a positive correlation, a negative correlation, or a correlation close to \(0 .\) Explain your choice. a. Weight of a car and gas mileage b. Size and selling price of a house c. Height and weight d. Height and number of siblings

A sample of automobiles traveling on a particular segment of a highway is selected. Each one travels at roughly a constant rate of speed, although speed does vary from auto to auto. Let \(x=\) Speed and \(y=\) Time needed to travel this segment. Would the sample correlation coefficient be closest to \(0.9,0.3,-0.3,\) or \(-0.9 ?\) Explain.

Medical researchers have noted that adoles- - Medical researchers have noted that adolles cent females are much more likely to deliver lowbirth-weight babies than are adult females. Because low-birth-weight babies have a higher mortality rate, a number of studies have examined the relationship between birth weight and mother's age. One such study is described in the article "Body Size and Intelligence in 6 -Year-Olds: Are Offspring of Teenage Mothers at Risk?" (Maternal and Child Health Journal [2009]: 847-856). The following data on maternal age (in years) and birth weight of baby (in grams) are consistent with summary values given in the article and also with data published by the National Center for Health Statistics. $$\begin{array}{lcccccc} \text { Mother's age } & 15 & 17 & 18 & 15 & 16 & 19 \\ \text { Birth weight } & 2289 & 3393 & 3271 & 2648 & 2897 & 3327 \end{array}$$ $$\begin{array}{lcccc} \text { Mother's age } & 17 & 16 & 18 & 19 \\ \text { Birth weight } & 2970 & 2535 & 3138 & 3573 \end{array}$$ a. If the goal is to learn about how birth weight is related to mother's age, which of these two variables is the response variable and which is the predictor variable? b. Construct a scatterplot of these data. Would it be reasonable to use a line to summarize the relationship between birth weight and mother's age? c. Find the equation of the least squares regression line. d. Interpret the slope of the least squares regression line in the context of this study. e. Does it make sense to interpret the intercept of the least squares regression line? If so, give an interpretation. If not, explain why it is not appropriate for this data set. (Hint: Think about the range of the \(x\) values in the data set.) f. What would you predict for birth weight of a baby born to an 18 -year-old mother? g. What would you predict for birth weight of a baby born to a 15 -year-old mother? h. Would you use the least squares regression equation to predict birth weight for a baby born to a 23 -year-old mother? If so, what is the predicted birth weight? If not, explain why.

Briefly explain why a small value of \(s_{e}\) is desirable in a regression setting.

For each of the following pairs of variables, indicate whether you would expect a positive correlation, a negative correlation, or a correlation close to \(0 .\) Explain your choice. a. Price and weight of an apple b. A person's height and the number of pets he or she has c. Time spent studying for an exam and score on the exam d. A person's weight and the time it takes him or her to run one mile

The relationship between hospital patient-to-nurse ratio and various characteristics of job satisfaction and patient care has been the focus of a number of research studies. Suppose \(x=\) Patient-to-nurse ratio is the predictor variable. For each of the following response variables, indicate whether you expect the slope of the least squares regression line to be positive or negative, and give a brief explanation for your choice. a. \(y=\) Measure of nurse's job satisfaction (higher values indicate higher satisfaction) b. \(y=\) Measure of patient satisfaction with hospital care (higher values indicate higher satisfaction) c. \(y=\) Measure of quality of patient care (higher values indicate higher quality)