A regression was run to determine if there Is a relationship between the happiness index (y) and life expectancy In years of a glven country (x). The results of the regresslon were: ý=a+bx a=-1.711 b=0.162 (a) Write the equation of the Least Squares Regression line of the form (b) Which is a possible value for the correlation coefficient, r? O-0.869 O-1.197 O1.197 O0.869 (C) If a country increases its life expectancy, the happiness index will O decrease Oincrease (d) If the life expectancy is increased by 4.5 years in a certain country, how much will the happiness Index change? Round to two decimal places.

A recent study showed that the hours a person exercised in a week affected the individual'sresting heart rate. It was computed that r = -.68 and the least squares regression line was?̂ = 83-1.4x, where x is the hours exercised and y is the resting heart rate.   d. What percentage of variability in resting heart rate can be explained by variability inhours exercised?

c) Show that the coefficient of determination, R², can also be obtained as the squared correlation between actual Y values and the Y values estimated from the regression model where Y is the dependent variable. Note that the coefficient of correlation between Y and X is Eyixi r = And also that ỹ = ŷ (18.75)

The​ least-squares regression equation is y=784.6x+12,431 where y is the median income and x is the percentage of 25 years and older with at least a​ bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7962.  In a particular​ region, 26.5 percent of adults 25 years and older have at least a​ bachelor's degree. The median income in this region is ​$29,889. Is this income higher or lower than what you would​ expect? Why?

It is known that the linear regression equation: y= -2.88+1.77x, with a coefficient of determination of 0.81. Based on the two information, the correlation coefficient is

The​ least-squares regression equation is y=620.6x+16,624 where y is the median income and x is the percentage of 25 years and older with at least a​ bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7004. Predict the median income of a region in which 30​% of adults 25 years and older have at least a​ bachelor's degree.

A biologist is interested in predicting the percentage increase in lung volume when inhaling (y) for a certain species of bird from the percentage of carbon dioxide in the atmosphere (x). Data collected from a random sample of 20 birds of this species were used to create the least-squares regression equation ŷ = 400-0.08x. Which of the following best describes the meaning of the slope of the least-squares regression line? (A) The percentage increase in lung volume when inhaling increases by 0.08 percent, on average, for every 1 percent increase in the carbon dioxide in the atmosphere. (B) The percentage of carbon dioxide in the atmosphere increases by 0.08 percent, on average, for every 1 percent increase in lung volume when inhaling. (C) The percentage increase in lung volume when inhaling decreases by 0.08 percent, on average, for every 1 percent increase in the carbon dioxide in the atmosphere. (D) The percentage of carbon dioxide in the atmosphere increases by 0.08 percent, on…

A regression was run to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x). The results of the regression were: ý=a+bx a=-1.692 b=0.117 (a) Write the equation of the Least Squares Regression line of the form (b) Which is a possible value for the correlation coefficient, r? O -0.649 O 1.32 O 0.649 O-1.32 (c) If a country increases its life expectancy, the happiness index will O increase O decrease (d) If the life expectancy is increased by 2.5 years in a certain country, how much will the happiness index change? Round to two decimal places. (e) Use the regression line to predict the happiness index of a country with a life expectancy of 75 years. Round to two decimal places.

There is a dataset of size n = 51 and is for the 50 states and the District of Columbia in the United States. The dependent variable is year 2002 birth rate per 1000 females 18 to 19 years old and independent variable is the violent crime rate (per 1000 population). A simple linear regression model is run with the results given below. What is the Pearson correlation coefficient between x and y variables? The R squared of the model? What kind of relationship there is?

A sample of 60 women is​ obtained, and their heights​ (in inches) and pulse rates​ (in beats per​ minute) are measured. The linear correlation coefficient is 0.263 and the equation of the regression line is y=17.9+0.940x​, where x represents height. The mean of the 60 heights is 63.3 in and the mean of the 60 pulse rates is 76.8 beats per minute. Find the best predicted pulse rate of a woman who is 67 in tall. Use a significance level of α=0.05.LOADING...  Click the icon to view the critical values of the Pearson correlation coefficient r.Question content area bottomPart 1The best predicted pulse rate of a woman who is 67 in tall is enter your response here beats per minute. ​(Type an integer or decimal rounded to two decimal places as​ needed.)