STAT CHAP 4.2
Consider the data set given in the accompanying table. Complete parts (a) through (c). (b) Find the equation of the line containing the points (−2,−2) and (2,5). (c) Graph the line found in part (b) on the scatter diagram. Choose the correct graph below.
D The equation of the line is y= 7/4x+ 3/2. B
A data set is given below. (a) Draw a scatter diagram. Comment on the type of relation that appears to exist between x and y. (b) Given that x=3.3333, sx=2.5033, y=3.9000, sy=2.0199, and r=−0.9572, determine the least-squares regression line. (c) Graph the least-squares regression line on the scatter diagram drawn in part (a).
ALL INFO IN REGRESSION C ; There appears to be a linear, negative relationship. b) y=negative 0.772−0.772x+ C
The data below represent commute times (in minutes) and scores on a well-being survey. Complete parts (a) through (d) below. (a) Find the least-squares regression line treating the commute time, x, as the explanatory variable and the index score, y, as the response variable. (b) Interpret the slope and y-intercept, if appropriate. Interpret the slope. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. Interpret the y-intercept. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (c) Predict the well-being index of a person whose commute time is 25 MIN (d) Suppose Barbara has a 15-minute commute and scores 67.4 on the survey. Is Barbara more "well-off" than the typical individual who has a 15-minute commute? Select the correct choice below and fill in the answer box to complete your choice.
y=-0.049x+69.063 For every unit increase in commute time, the index score falls by 0.049 on average. For a commute time of zero minutes, the index score is predicted to be 69.063 The predicted index score is 67.8 No, Barbara is less well-off because the typical individual who has a 15-minute commute scores 68.3
The given data represent the total compensation for 10 randomly selected CEOs and their company's stock performance in 2009. Analysis of this data reveals a correlation coefficient of r=−0.1790. What would be the predicted stock return for a company whose CEO made $15 million? What would be the predicted stock return for a company whose CEO made $25 million?
17.3 17.3
Suppose the line y=2.8333x−22.4967 describes the relation between the club-head speed (in miles per hour), x and the distance a golf ball travels (in yards), y. (a) Predict the distance a golf ball will travel if the club-head speed is 100 mph. (b) Suppose the observed distance a golf ball traveled when the club-head speed was 100 mph was 265 yards. What is the residual?
260.8 265-260.8=4.2
(a) By hand, draw a scatter diagram treating x as the explanatory variable and y as the response variable. Choose the correct scatter diagram below. b) Find the equation of the line containing the points (50,68) and (80,43). (c) Graph the line found in part (b) on the scatter diagram. Choose the correct graph below. (d) By hand, determine the least-squares regression line. (e) Graph the least-squares regression line on the scatter diagram. Choose the correct graph below. (f) Compute the sum of the squared residuals for the line found in part (b). (g) Compute the sum of the squared residuals for the least-squares regression line found in part (d). h) Comment on the fit of the line found in part (b) versus the least-squares regression line found in part (d).
b y=-5/6x+329/3 d y=-0.72x+104.4 c 61 36.4 The line in part (b) passes through the most points. The line in part (d) minimizes the sum of the squared residuals, thus being the best-fitting line.
Explain what each point on the least-squares regression line represents.
Each point on the least-squares regression line represents the predicted y-value at the corresponding value of x.
Is there a relation between the age difference between husband/wives and the percent of a country that is literate? Researchers found the least-squares regression between age difference (husband age minus wife age), y, and literacy rate (percent of the population that is literate), x, is y=−0.0545x+8.4. The model applied for 22≤x≤100. Complete parts (a) through (e) below. (a) Interpret the slope. Select the correct choice below and fill in the answer box to complete your choice. (b) Does it make sense to interpret the y-intercept? Explain. Choose the correct answer below. (c) Predict the age difference between husband/wife in a country where the literacy rate is 29 percent. (d) Would it make sense to use this model to predict the age difference between husband/wife in a country where the literacy rate is 17% (e) The literacy rate in a country is 99% and the age difference between husbands and wives is 2 years. Is this age difference above or below the average age difference among all countries whose literacy rate is 99%? Select the correct choice below and fill in the answer box to complete your choice.
For every unit increase in literacy rate, the age difference falls by 0.0545 units, on average. No—it does not make sense to interpret they-intercept because anx-value of 0 is outside the scope of the model. 6.8 No—it does not make sense because anx-value of 17 is outside the scope of the model. BELOW; 3.0 DIFFERENCE OF 99%
A pediatrician wants to determine the relation that exists between a child's height, x, and head circumference, y. She randomly selects 11 children from her practice, measures their heights and head circumferences and obtains the accompanying data. Complete parts (a) through (e). a) Find the least-squares regression line treating height as the explanatory variable and head circumference as the response variable. (b) Use the regression equation to predict the head circumference of a child who is 25 inches tall. (c)Compute the residual based on the observed head circumference of the 25-inch-tall child in the table. Is the head circumference of this child above average or belowaverage? d) Draw the least-squares regression line on the scatter diagram of the data and label the residual from part (c). Choose the correct graph below. Is the head circumference of this child above average or below average (e) Notice that two children are 26.75 inches tall. One has a head circumference of 17.3 inches; the other has a head circumference of 17.5 inches. How can this be?
STAT-REGRESSION-LINEAR- COMPUTE FIND WHERE IT SAYS INTERCEPT AND SLOPE ENTER 25 FOR PERDICTED X 95% CI MEAN- PRED Y. B BELOW AVERAGE For children who are 26.75 inches tall, head circumference varies.
One of the biggest factors in determining the value of a home is the square footage. The accompanying data represent the square footage and selling price (in thousands of dollars) for a random sample of homes for sale in a certain region. Complete parts (a) through (h) below. (a) Which variable is the explanatory variable? (b) Draw a scatter diagram of the data. Choose the correct scatter diagram below. c) Determine the linear correlation coefficient between square footage and asking price. (d) Is there a linear relation between square footage and asking price? (e) Find the least-squares regression line treating square footage as the explanatory variable. (f) Interpret the slope. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (g) Is it reasonable to interpret the y-intercept? Why? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (h) One home that is 1435 square feet is sold for $210 thousand. Is this home's price above or below average for a home of this size?
Square Footage C R= 0.903 YES Y=0.160X +5.6 For every additional square foot, the selling price increases by 0.160 thousand dollars, on average. No—a house of 0 square feet is not possible and outside the scope of the model. The home's price is below the average price. The average price of a home that is 1435 square feet is $235 thousand.
A student at a junior college conducted a survey of 20 randomly selected full-time students to determine the relation between the number of hours of video game playing each week, x, and grade-point average, y. She found that a linear relation exists between the two variables. The least-squares regression line that describes this relation is y=−0.0578x+2.9274. (a) Predict the grade-point average of a student who plays video games 8 hours per week. b) Interpret the slope. (c) If appropriate, interpret the y-intercept. (d) A student who plays video games 7 hours per week has a grade-point average of 2.63. Is the student's grade-point average above or below average among all students who play video games 7 hours per week?
The predicted grade-point average is 2.47 For each additional hour that a student spends playing video games in a week, the grade-point average will decrease by 0.0578 points, on average. The grade-point average of a student who does not play video games is 2.9274. The student's grade-point average is above average for those who play video games 7 hours per week.
Which of the following is true of the least-squares regression line y=b1x+b0?
The sign of the linear correlation coefficient, r, and the sign of the slope of the least-squares regression line, b1, are the same. The least-squares regression line always contains the point x,y. The predicted value of y, y, is an estimate of the mean value of the response variable for that particular value of the explanatory variable. The least-squares regression line minimizes the sum of squared residuals.
Consider the data set given in the accompanying table. Complete parts (a) through (d). (a) Determine the least-squares regression line. Choose the correct answer below. (b) Graph the least-squares regression line on the scatter diagram. Choose the correct graph below. (c) The equation of the line containing the points (−2,−2) and (2,5) is y=1.75x+1.5. Compute the sum of the squared residuals of the given data set for this line. (d) Compute the sum of the squared residuals of the given data set for the least-squares regression line found in part (a).
The least-squares regression line is y=1.8x+1.2. d The sum of the squared residuals for the line containing the points (−2,−2) and (2,5) is 0.875 GO TO DATA--COMPUTE EXPRESSION- WRITE FOR EXAMPLE (y-(1.75*x+1.5))^2 COMPUTE THEN GO TO STAT SUMMARY CHOOSE SUM YOU CAN FIND THIS IN THE REGRESSION RESULTS ERROR-SS
Complete parts (a) through (h) for the data below. (a) By hand, draw a scatter diagram treating x as the explanatory variable and y as the response variable. Choose the correct scatter diagram below. (b) Find the equation of the line containing the points (2,3) and (7,18). (c) Graph the line found in part (b) on the scatter diagram. Choose the correct graph below. (d) By hand, determine the least-squares regression line. (e) Graph the least-squares regression line on the scatter diagram. Choose the correct graph below. (f) Compute the sum of the squared residuals for the line found in part (b). g) Compute the sum of the squared residuals for the least-squares regression line found in part (d). (h) Comment on the fit of the line found in part (b) versus the least-squares regression line found in part (d).
a y=3x+(-3) c y=3.047x-3.605 b 4 3.163 The line in part (b) passes through the most points. The line in part (d) minimizes the sum of the squared residuals, thus being the best-fitting line.
