4. maria also wants to study the relationship between the weight of puppies at birth and their adult weight (at two years old). she collected data from five randomly selected small-breed dogs and displayed the data in the table.
birth weight (pounds) adult weight (pounds)
1.5 10
3 17
1 8
2.5 14
0.75 5
part a. use the data in the table to create a scatterplot. (5 points)
part b. look at the scatterplot that you drew in part a. which regression equation (linear, exponential, or quadratic) do you think would be the best model for these data? to you decide, think about the adult weight you would expect if the birth weight were larger — say, 10 pounds. would you expect the pattern in the scatterplot to continue? to grow exponentially? to change direction? explain your answer. (2 points)
part c. perform a linear regression and interpret the results.
a. use a calculator to perform a linear regression. round the values your calculator gives you for a and b to the nearest hundredth. (2 points)
y = +
b. what is the slope of the regression equation? what does this mean in terms of the birth weight and adult weight? (2 points)
c. what is the value of the correlation coefficient? (1 point)
d. describe the correlation in terms of strength (weak or strong) and direction (positive or negative). (2 points)
part d. analyze the residuals.
birth weight
(pounds)
adult weight
(pounds)
predicted
adult weight
residual
1.5
10
3
17
1
8
2.5
14
0.75
5
a. use the linear regression equation from part c to calculate the predicted adult weight for each birth weight. round to the nearest hundredth. enter these in the third column of the table. (2.5 points)
b. find the residual for each birth weight. round to the nearest hundredth. enter these in the fourth column of the table. (2.5 points)
c. plot the residuals. (3 points)
d. based on the residuals, is your regression line a reasonable model for the data? why or why not? (2 points)