Stat Ch 10.2 HW
What is a residual?
A residual is a value of y−^y, which is the difference between an observed value of y and a predicted value of y.
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 132 to 193 cm and weights of 40 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x=167.22 cm, y=81.40 kg, r=0.403, P-value=0.000, and y=−106+1.01x. Find the best predicted value of y (weight) given an adult male who is 172 cm tall. Use a 0.10 significance level.
The best predicted value of ^y for an adult male who is 172 cm tall is 67.7267.72 kg.
For 50 randomly selected speed dates, attractiveness ratings by males of their female date partners (x) are recorded along with the attractiveness ratings by females of their male date partners (y); the ratings range from 1 to 10. The 50 paired ratings yield x=6.4, y=6.0, r=−0.212, P-value=0.140, and y=7.49−0.235x. Find the best predicted value of ^y (attractiveness rating by female of male) for a date in which the attractiveness rating by the male of the female is x=7. Use a 0.10 significance level.
The best predicted value of ^y when x=7 is 66.
Suppose IQ scores were obtained for 20 randomly selected sets of siblings. The 20 pairs of measurements yield x=99.4, y=98, r=0.848, P-value=0.000, and y=8.98+0.9x, where x represents the IQ score of the younger child. Find the best predicted value of y given that the younger child has an IQ of 95? Use a significance level of 0.05.
The best predicted value of y is ^94.48 ^y = 8.98 + 0.9(99.4) = 94.48
Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line. x y 9 9.82 14 9.52 4 2.52 10 10.37 6 6.36 5 4.59 12 10.56 8 8.97 13 10.19 7 7.81 11 10.61 Identify a characteristic of the data that is ignored by the regression line.
The data has a pattern that is not a straight line.
What is the difference between the following two regression equations? ^y=b0+b1x y = β0 + β1x
The first equation is for sample data; the second equation is for a population.
In what sense is the regression line the straight line that "best" fits the points in a scatterplot?
The regression line has the property that the sum of squares of the residuals is the lowest possible sum.
Different hotels in a certain area are randomly selected, and their ratings and prices were obtained online. Using technology, with x representing the ratings and y representing price, we find that the regression equation has a slope of 120 and a y-intercept of −370. What does the symbol ^y represent?
The symbol ^y represents the predicted value of price.
What is the relationship between the linear correlation coefficient r and the slope b1 of a regression line?
The value of r will always have the same sign as the value of b1.
Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line. x y 10 7.65 8 7.04 13 13.03 10 6.96 10 7.5 13 8.8 5 5.83 4 5.34 11 8.53 6 6.55 6 6.01 Identify a characteristic of the data that is ignored by the regression line.
There is an influential point that strongly affects the graph of the regression line.
Different hotels in a certain area are randomly selected, and their ratings and prices were obtained online. Using technology, with x representing the ratings and y representing price, we find that the regression equation has a slope of 120 and a y-intercept of −370. What is the equation of the regression line? Select the correct choice below and fill in the answer boxes to complete your choice.
^y=−370+120x
Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line. x y 9 9.82 14 9.52 4 2.52 10 10.37 6 6.36 5 4.59 12 10.56 8 8.97 13 10.19 7 7.81 11 10.61
y=2.00+0.7x
Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line. x y 10 7.65 8 7.04 13 13.03 10 6.96 10 7.5 13 8.8 5 5.83 4 5.34 11 8.53 6 6.55 6 6.01 Find the equation of the regression line.
y=2.73+0.555x