3. maria is a veterinarian. she wants to know how the weight of a puppy is related to its length. to find out, maria randomly selected 10 puppies that are two months old. she recorded the length and weight of each puppy in the table below.
part a. the data from the table are shown on the scatterplot. draw an estimated line of best fit through the data points. (3 points)
part b. use the scatterplot to answer these questions.
a. what kind of correlation exists between the length and weight of the puppies? explain. (2 points)
strong positive-linear correlation.
when the length of the puppies increases, they increase their weight simultaneously.
b. identify two points on the line of best fit that you drew in part a. use the two points to find the equation of the line. write the equation of the best fit line in slope-intercept form. show your work. (4 points: 1 point for identifying the coordinates of two points, 1 point for slope, 1 point for b-value, and 1 point for showing work)
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)
5. decide whether each statement is true or false. (1 point each)
a. t/f: if there is a strong correlation between two variables, the correlation coefficient will be close to –1 or 1.
b. t/f: if there is a negative correlation between two variables, the slope of the regression line will be positive.
c. t/f: if there is a strong correlation between two variables, there is a cause-and-effect relationship.
d. t/f: the best model for data that change direction is a linear model.
e. t/f: a regression line is useful for predicting unknown values within the range of the observed data values.