Please help me answer PRACTICE EXERCISE with SOLUTION

10. Construction standards specify the strength of concrete 28 days after it is poured. For 30 samples of various types of concrete the strength x after 3 days and the strength y after 28 days (both in hundreds of pounds per square inch) were measured. The sample data are summarized by the following information. N = 30 Ex = 501.6 Exy = 23,246.55 Ey? = 61,980.14 Zy = 1338.8 Ex2 = 8724.74 a. Compute the least squares regression line. b. Interpret the value of the slope of the least squares regression line in the context of the problem. c. Estimate the average concentration of the active ingredient in the blood in men after consuming 1 ounce of the medication. Chapter Summary Two variables x and y have a linear relationship if points plotted from (x,y) pairs lie exactly along a single straight line. In practice it is common for two variables to exhibit a relationship that is close to linear but which contains an element, possibly large, of randomness. The linear correlation coefficient measures the strength and direction of the linear relationship between two variables x and y. The sign of the linear correlation coefficient indicates the direction of the linear relationship between x and y. When r is near 1 or - 1 the linear relationship is strong; when it is near 0 the linear relationship is weak. A straight line that fits a data set is measured by the sum of the squared errors. The least squares regression line is the line that best fits the data. Its slope and y-intercept are computed from the data using formulas. The slope m of the least squares regression line estimates the size and direction of the mean change in the dependent variable y when the independent variable x is increased by one unit. The sum of the squared errors SSE of the least squares regression line can be computed using a formula, without having to compute all the individual errors. 172 STATISTICS AND PROBABILITYa. Compute the least squares regression line. b. On average, how many new words does a child from 13 to 18 months old learn each month? Explain. c. Estimate the average vocabulary of all 16-month-old children. 7. The age x in months and vocabulary y were measured for six children, with the results shown in the table. X 20 23 30 37 35 45 51 55 60 63 y 72 71 73 74 74 73 72 79 75 77 a. Compute the least squares regression line. b. Estimate the average resting heart rate of all 40-year-old men. c. Estimate the average resting heart rate of all newborn baby boys. Comment on the validity of the estimate. 8. The advertising expenditure x and sales y in thousands of dollars for a small retail business in its first eight years in operation are shown in the table. X 1.4 1.6 1.6 2.0 2.0 2.2 2.4 2.6 y 180 184 190 220 186 215 205 240 . Compute the least squares regression line. b. On average, for each additional thousand dollars spent on advertising, how does revenue change? Explain. c. Estimate the revenue if $2,500 is spent on advertising next year. 9. Fifty male subjects drank a measured amount x (in ounces) of a medication and the concentration y (in percent) in their blood of the active ingredient was measured 30 minutes later. The sample data are summarized by the following information. N = 50 Ex = 112.5 Exy = 15.255 Ex2 = 356.25 Ey2 = 0.667 Ey = 4.83 0