Consider the following table of data. 1 2 4 9. y 1 2 4 -20 (a) Calculate the least squares line and the correlation coefficient. (b) Repeat part (a), but this time delete the last point. (c) Draw a graph of the data, and use it to explain the dramatic difference between the answers to parts (a) and (b). 3. 3.
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- An article included a summary of findings regarding the use of SAT I scores, SAT II scores, and high school grade point average (GPA) to predict first-year college GPA. The article states that "among these, SAT II scores are the best predictor, explaining 17 percent of the variance in first-year college grades. GPA was second at 15.2 percent, and SAT I was last at 13.1 percent." If the data from this study were used to fit a least squares line with y = first-year college GPA and x = high school GPA, what would the value of r2 have been? R2 ____________________%The amount (in millions of dollars) of used autos sold online in a certain country from 2011 to 2015 is given in the following table (x = 0 corresponds to 2011). Year, x 0 1 2 3 4 Sales, y 12.9 13.9 14.65 15.25 15.85 (a) Find an equation of the least-squares line for these data.y = (b) Use the result of part (a) to estimate the sales of used autos online in 2016, assuming that the predicted trend continued. (Round your answer to one decimal place.)$ millionA simple random sample of 100 men aged 25–34 averaged 70 inches in height, and had astandard deviation of 3 inches. Their incomes averaged $34,900 and had a standarddeviation of $17,200. Fill in the blank: From the least-squares line, we would predict thatthe income of a man 70 inches tall would be _____.a) less than $34,900.b) greater than $34,900.c) equal to $34,900.d) We cannot tell unless we know the correlation.
- Suppose a doctor measures the height, x, and head circumference, y, of 11 children and obtains the data below. The correlation coefficient is 0.899 and the least squares regression line is y=0.185x+12.276. Complete parts (a) and (b) below. Height, x 27.75 25.75 26.75 25.75 28 26.5 25.75 26.75 27 27.25 27.25 Head Circumference, y 17.4 17.1 17.2 16.9 17.4 17.1 17.1 17.3 17.3 17.3 17.4 (a) Compute the coefficient of determination, R2. R2=nothing% (Round to one decimal place as needed.) (b) Interpret the coefficient of determination. Approximately nothing% of the variation in ▼ height head circumference is explained by the least-squares regression model. (Round to one decimal place as needed.)The following table shows the percent of water and the number of calories in various canned soups to which 100 g of water are added. (show all the necessary solution) Percent Water in Soups % Water Calories 83.3 28 92.3 26 91.9 39 89.4 57 89.5 57 90.5 36 91.9 32 91.7 32 a. Find the equation of the least squares line for the data. b. Use the equation in part a to find the expected number of calories in a soup that is 87% water. c. Determine the correlation coefficient of the data.When we use a least-squares line to predict y values for x values beyond the range of x values found in the data, are we extrapolating or interpolating? Are there any concerns about such predictions?