(6 points; Chapter 8.1 ) In an observational study, data about 100 diamond rings was\ collected, including the variables carat of the diamond (a measure of quality, ranging from\ 0.24 to 2.71 ) and price (ranging from

$413

to

$17,151

). The scatterplot below shows the\ carat on the x-axis (horizontal) and the price on the v-axis (vertical).\ a. Define the response variable and the explanatory variable.\ b. Which of the following is a reasonable estimate of correlation between these two\ variables? (Choose one of the four options below)\ (a) 0.2\ (b) -0.8\ (c) 0.9\ (d) 1.5\ c. A linear model (applied in R) was used to describe the relationship between the two\ variables. Use the output below to answer the following three questions (i-iii).\ i. Write the regression equation\ ii. Predict the price of a 1.3 carat diamond\ iii. The diamond represented by the data point circled in red on the scatterplot\ above is a 2.06 carat diamond with a price tag of

$6,091

. What is the value of\ the residual associated with this data point?\

>1m

(price carat, data

=

use_diamonds)\ Ca11:\ 1m(formula = price

carat, data

=

use_diamonds)\ Coefficients:\ (Intercept)\ carat\

-1969

\ 7247

3. (6 points; Chapter 8.1 ) In an observational study, data about 100 diamond rings was collected, including the variables carat of the diamond (a measure of quality, ranging from 0.24 to 2.71 ) and price (ranging from $413 to $17,151 ). The scatterplot below shows the 2/3 carat on the x-axis (horizontal) and the price on the y-axis (vertical). a. Define the response variable and the explanatory variable. b. Which of the following is a reasonable estimate of correlation between these two variables? (Choose one of the four options below) (a) 0.2 (b) -0.8 (c) 0.9 (d) 1.5 c. A linear model (applied in R) was used to describe the relationship between the two variables. Use the output below to answer the following three questions (i - iii). i. Write the regression equation ii. Predict the price of a 1.3 carat diamond iii. The diamond represented by the data point circled in red on the scatterplot above is a 2.06 carat diamond with a price tag of $6,091. What is the value of the residual associated with this data point? >1m (price carat, data = use_diamonds) Ca11: 1m (formula = price carat, data = use_diamonds) Coefficients: (Intercept) carat 1969 7247