A random sample of 15 college soccer players were selected to investigate the relationship between heart rate and maximal oxygen uptake. The heart rate and maximal oxygen uptake were recorded for each player during a training session. A regression analysis of the data was conducted, where heart rate is the explanatory variable and maximal oxygen uptake is the response variable. If a 95 percent confidence interval is constructed for the slope of the population regression line, which of the following is a condition that must be checked?   A)The true relationship between heart rate and maximal oxygen uptake is linear. B)The correlation between heart rate and maximal oxygen uptake is not equal to zero. C)The confidence interval is not biased. D).The point (x_,y_) falls on the regression line.  The X and Y have a line on top. E)The slope is not equal to zero.

A ski resort asked a random sample of guests to rate their satisfaction on various attributes of their visit on a scale of 1-5 with 1 = very unsatisfied and 5 = very satisfied. The estimated regression model was Y=overall satisfaction score, X₁ = lift line wait, X₂ = amount of ski trail grooming, X3 = safety patrol visibility, and X4 = friendliness of guest services. Predictor Intercept LiftWait AmountGroomed SkiPatrolVisibility FriendlinessHosts (a) Write the fitted regression equation. (Round your answers to 4 decimal places. Negative values should be indicated by a minus sign.) |ŷ = + (b) Interpret each coefficient. Overall satisfaction Coefficient 2.9233 0.1544 0.2403 0.0645 -0.1291 LiftWait + *AmountGroomed + with an increase in satisfaction for each individual predictor except for friendliness of hosts. * SkiPatrolVisibility + * FriendlinessHosts

Researchers are examining the relationship between hours of sleep and athletic performance among college athletes. Athletic performance will be measured on a numeric scale, with greater numbers indicating better performance. The researchers expect that the more hours the athletes sleep, the better they will perform. Assuming all conditions for inference are met, the researchers will create a 95 percent confidence interval for the slope of the regression line for predicting athletic performance from amount of sleep. For which of the following would the confidence interval support the researchers' expectations? (A) The confidence interval includes only positive values. (B) The confidence interval includes only negative values. (C) The confidence interval has a width less than 1. (D) The confidence interval has a width greater than 1. (E) The confidence interval includes the value 0.

In this question, we investigate the relationship between the top (maximum) speed (mph) and maximum height for a random sample of roller coasters in the United States. Here is the scatterplot and a summary of the simple linear regression model.   Construct a 95% confidence interval for the true slope of the regression line and interpret your confidence interval in context.