Unit 2 test: Exploring Two-Variable Data

What proportion of seniors prefer the online class?

Which statement about these students is correct?

A researcher wants to see whether the amount of fertilizer applied to a plot helps predict the plot's tomato yield. Which is correct?

Which description best fits this scatterplot of $10$ students?

The correlation between $x$ and $y$ for a data set is $r = 0.58$. A new variable is defined by $w = 10 - 3y$. What is the correlation between $x$ and $w$?

A scatterplot shows a strong curved pattern that rises and then falls. Which value of $r$ is most plausible, and why?

For a sample of apartments, floor area $x$ (hundreds of square feet) has $\bar{x} = 10$ and $s_x = 2.5$, monthly rent $y$ (hundreds of dollars) has $\bar{y} = 40$ and $s_y = 6$, and $r = 0.75$. Find the slope of the least-squares regression line.

Using the apartment summary statistics and the slope $b = 1.8$, find the $y$-intercept of the least-squares regression line.

Using the apartment model $\hat{y} = 22 + 1.8x$, an apartment with $x = 12$ rents for $y = 41$ (both in hundreds). Find its residual.

A regression of weekly sales (dollars) on advertising spending (dollars) gives this output. Which is the least-squares regression line?

$S = 415.7 \qquad \text{R-Sq} = 76.0\%$

For the advertising output above, find the correlation $r$, rounded to three decimal places.

For the advertising regression, which is the correct interpretation of $S = 415.7$?

Here is the residual plot from a linear regression. What does it indicate?

A data set's $x$-values range from $2$ to $10$, except for one point at $x = 40$ that lies far below the pattern of the others. Removing that point changes the slope from $0.4$ to $2.1$. Which description is best?

A researcher models the number of downloads $y$ of an app (in thousands) in week $x$ with $\widehat{\log y} = 0.8 + 0.25x$. Predict the number of downloads (in thousands) in week $4$. Round to the nearest tenth.