This question tests informally fitting a straight line to a scatter plot showing linear association and assessing fit by judging point closeness to the line. Linear association (points trending along straight direction) modeled by straight line: fit line informally by drawing through middle of point cloud, balancing points above and below (roughly equal numbers each side). Assess fit: good fit has most points close to line (small vertical distances from points to line—predictions accurate), poor fit has points far from line (large vertical deviations—predictions less reliable). Line captures linear trend, allows prediction (use line to estimate y for new x). For example, in a scatter plot of chores vs allowance, comparing two lines where one has smaller vertical distances (1-2 dollars away) vs larger (5-6 away), the one with smaller residuals fits better. Student 1’s line is better, because the vertical distances (residuals) from the points to the line are smaller for most points. Common errors include preferring steeper lines or thinking farther distances are more accurate. Fitting: (1) observe trend direction (upward→positive slope, downward→negative), (2) estimate center of points (where is middle of cloud?), (3) draw line through center following trend (balance points above/below), (4) verify reasonable (does line capture pattern? points fairly close?). Assessing: (1) observe vertical distances from points to line (how far off?), (2) count how many close (within 1-2 grid squares) vs far (5+ squares away), (3) judge: most close=good fit, many far=poor fit, (4) compare alternatives (if multiple lines, which has points closer on average?). Real data: rarely perfect (scatter means variability, line approximates), outliers exist (don't force line to hit outlier—fit majority), linear adequate if points roughly straight trend (even if imperfect). Mistakes: line through outlier ignoring majority, all points above or below (unbalanced), fit by horizontal distance (wrong—vertical distance for y-prediction matters), claiming poor fit is good or vice versa.

This question tests informally fitting a straight line to a scatter plot showing linear association and assessing fit by judging point closeness to the line. Linear association (points trending along straight direction) modeled by straight line: fit line informally by drawing through middle of point cloud, balancing points above and below (roughly equal numbers each side). Assess fit: good fit has most points close to line (small vertical distances from points to line—predictions accurate), poor fit has points far from line (large vertical deviations—predictions less reliable). Line captures linear trend, allows prediction (use line to estimate y for new x). For example, in a scatter plot of minutes practiced vs free throws made showing upward linear trend, using the line y ≈ 0.8x + 2 to predict for x=20 gives y ≈ 18, assessing fit by how well it approximates actual points. The correct prediction is about 18, calculated as 0.8*20 + 2 = 18, using the line for estimation. Common errors include miscalculating the prediction like choosing 16 (forgetting to add 2) or 22 (using wrong slope). Fitting: (1) observe trend direction (upward→positive slope, downward→negative), (2) estimate center of points (where is middle of cloud?), (3) draw line through center following trend (balance points above/below), (4) verify reasonable (does line capture pattern? points fairly close?). Assessing: (1) observe vertical distances from points to line (how far off?), (2) count how many close (within 1-2 grid squares) vs far (5+ squares away), (3) judge: most close=good fit, many far=poor fit, (4) compare alternatives (if multiple lines, which has points closer on average?). Real data: rarely perfect (scatter means variability, line approximates), outliers exist (don't force line to hit outlier—fit majority), linear adequate if points roughly straight trend (even if imperfect). Mistakes: line through outlier ignoring majority, all points above or below (unbalanced), fit by horizontal distance (wrong—vertical distance for y-prediction matters), claiming poor fit is good or vice versa.

This question tests informally fitting a straight line to a scatter plot showing linear association and assessing fit by judging point closeness to the line. Linear association (points trending along straight direction) modeled by straight line: fit line informally by drawing through middle of point cloud, balancing points above and below (roughly equal numbers each side). Assess fit: good fit has most points close to line (small vertical distances from points to line—predictions accurate), poor fit has points far from line (large vertical deviations—predictions less reliable). Line captures linear trend, allows prediction (use line to estimate y for new x). For example, in a scatter plot of texts sent vs battery used with one outlier, fitting line through the main cluster's center, assessing fit by closeness of majority points, ignoring the outlier's pull. The best approach is to draw the line to fit the main cluster of points, without letting the one outlier determine the slope. Common errors include drawing through the outlier only or using a curved or horizontal line. Fitting: (1) observe trend direction (upward→positive slope, downward→negative), (2) estimate center of points (where is middle of cloud?), (3) draw line through center following trend (balance points above/below), (4) verify reasonable (does line capture pattern? points fairly close?). Assessing: (1) observe vertical distances from points to line (how far off?), (2) count how many close (within 1-2 grid squares) vs far (5+ squares away), (3) judge: most close=good fit, many far=poor fit, (4) compare alternatives (if multiple lines, which has points closer on average?). Real data: rarely perfect (scatter means variability, line approximates), outliers exist (don't force line to hit outlier—fit majority), linear adequate if points roughly straight trend (even if imperfect). Mistakes: line through outlier ignoring majority, all points above or below (unbalanced), fit by horizontal distance (wrong—vertical distance for y-prediction matters), claiming poor fit is good or vice versa.

This question tests informally fitting a straight line to a scatter plot showing linear association and assessing fit by judging point closeness to the line. Linear association (points trending along straight direction) modeled by straight line: fit line informally by drawing through middle of point cloud, balancing points above and below (roughly equal numbers each side). Assess fit: good fit has most points close to line (small vertical distances from points to line—predictions accurate), poor fit has points far from line (large vertical deviations—predictions less reliable). Line captures linear trend, allows prediction (use line to estimate y for new x). For example, in a scatter plot of distance biked vs time showing upward linear trend at steady pace, fitting line through approximate center sloping upward, assessing fit by observing most points close to the line (good fit for linear relationship). The best explanation is that a straight line is reasonable because the points follow a roughly straight upward trend, showing a linear relationship. Common errors include thinking lines must hit every point or only connect extremes. Fitting: (1) observe trend direction (upward→positive slope, downward→negative), (2) estimate center of points (where is middle of cloud?), (3) draw line through center following trend (balance points above/below), (4) verify reasonable (does line capture pattern? points fairly close?). Assessing: (1) observe vertical distances from points to line (how far off?), (2) count how many close (within 1-2 grid squares) vs far (5+ squares away), (3) judge: most close=good fit, many far=poor fit, (4) compare alternatives (if multiple lines, which has points closer on average?). Real data: rarely perfect (scatter means variability, line approximates), outliers exist (don't force line to hit outlier—fit majority), linear adequate if points roughly straight trend (even if imperfect). Mistakes: line through outlier ignoring majority, all points above or below (unbalanced), fit by horizontal distance (wrong—vertical distance for y-prediction matters), claiming poor fit is good or vice versa.

This question tests informally fitting a straight line to a scatter plot showing linear association and assessing fit by judging point closeness to the line. Linear association (points trending along straight direction) modeled by straight line: fit line informally by drawing through middle of point cloud, balancing points above and below (roughly equal numbers each side). Assess fit: good fit has most points close to line (small vertical distances from points to line—predictions accurate), poor fit has points far from line (large vertical deviations—predictions less reliable). Line captures linear trend, allows prediction (use line to estimate y for new x). For example, in a scatter plot of push-ups vs time showing downward linear trend, fitting line through approximate center sloping downward, assessing fit by observing most points within ±5 seconds of line vertically (good fit), or comparing two possible lines where one passes closer to majority of points (better fit). The correct choice is Line A, because it goes through the middle of the point cloud and leaves about the same number of points above and below, capturing the negative trend. Common errors include prioritizing extreme points or expecting the line to pass through every point. Fitting: (1) observe trend direction (upward→positive slope, downward→negative), (2) estimate center of points (where is middle of cloud?), (3) draw line through center following trend (balance points above/below), (4) verify reasonable (does line capture pattern? points fairly close?). Assessing: (1) observe vertical distances from points to line (how far off?), (2) count how many close (within 1-2 grid squares) vs far (5+ squares away), (3) judge: most close=good fit, many far=poor fit, (4) compare alternatives (if multiple lines, which has points closer on average?). Real data: rarely perfect (scatter means variability, line approximates), outliers exist (don't force line to hit outlier—fit majority), linear adequate if points roughly straight trend (even if imperfect). Mistakes: line through outlier ignoring majority, all points above or below (unbalanced), fit by horizontal distance (wrong—vertical distance for y-prediction matters), claiming poor fit is good or vice versa.

Tests informally fitting straight line to scatter plot showing linear association and assessing fit by judging point closeness to line. Linear association (points trending along straight direction) modeled by straight line: fit line informally by drawing through middle of point cloud, balancing points above and below (roughly equal numbers each side). Assess fit: good fit has most points close to line (small vertical distances from points to line—predictions accurate), poor fit has points far from line (large vertical deviations—predictions less reliable). Line captures linear trend, allows prediction (use line to estimate y for new x). For example, in a scatter plot of practice shots vs free-throw percentage showing upward linear trend, fitting line through approximate center sloping upward, assessing fit by observing most points close to the line vertically (good fit), or comparing two possible lines where one passes closer to majority of points (better fit). The correct line is Line A (y=4x+40) because it goes through the middle of the point cloud and has smaller vertical distances for most points (choice A). A common error is choosing a steeper line because it reaches higher values faster or passes through the highest point, but the best fit balances closeness to all points, not extremes. Fitting: (1) observe trend direction (upward→positive slope, downward→negative), (2) estimate center of points (where is middle of cloud?), (3) draw line through center following trend (balance points above/below), (4) verify reasonable (does line capture pattern? points fairly close?). Assessing: (1) observe vertical distances from points to line (how far off?), (2) count how many close (within 1-2 grid squares) vs far (5+ squares away), (3) judge: most close=good fit, many far=poor fit, (4) compare alternatives (if multiple lines, which has points closer on average?). Real data: rarely perfect (scatter means variability, line approximates), outliers exist (don't force line to hit outlier—fit majority), linear adequate if points roughly straight trend (even if imperfect). Mistakes: line through outlier ignoring majority, all points above or below (unbalanced), fit by horizontal distance (wrong—vertical distance for y-prediction matters), claiming poor fit is good or vice versa.

Tests informally fitting straight line to scatter plot showing linear association and assessing fit by judging point closeness to line. Linear association (points trending along straight direction) modeled by straight line: fit line informally by drawing through middle of point cloud, balancing points above and below (roughly equal numbers each side). Assess fit: good fit has most points close to line (small vertical distances from points to line—predictions accurate), poor fit has points far from line (large vertical deviations—predictions less reliable). Line captures linear trend, allows prediction (use line to estimate y for new x). For example, in a scatter plot of text messages vs phone minutes with upward trend, a downward-sloping line fails to capture the positive association. The best critique is that the slope is the wrong direction; the line should have a positive slope to match the upward trend (choice A). A common error is accepting a negative slope because it balances points or crosses the y-axis, but the slope must match the trend direction. Fitting: (1) observe trend direction (upward→positive slope, downward→negative), (2) estimate center of points (where is middle of cloud?), (3) draw line through center following trend (balance points above/below), (4) verify reasonable (does line capture pattern? points fairly close?). Assessing: (1) observe vertical distances from points to line (how far off?), (2) count how many close (within 1-2 grid squares) vs far (5+ squares away), (3) judge: most close=good fit, many far=poor fit, (4) compare alternatives (if multiple lines, which has points closer on average?). Real data: rarely perfect (scatter means variability, line approximates), outliers exist (don't force line to hit outlier—fit majority), linear adequate if points roughly straight trend (even if imperfect). Mistakes: line through outlier ignoring majority, all points above or below (unbalanced), fit by horizontal distance (wrong—vertical distance for y-prediction matters), claiming poor fit is good or vice versa.

Tests informally fitting straight line to scatter plot showing linear association and assessing fit by judging point closeness to line. Linear association (points trending along straight direction) modeled by straight line: fit line informally by drawing through middle of point cloud, balancing points above and below (roughly equal numbers each side). Assess fit: good fit has most points close to line (small vertical distances from points to line—predictions accurate), poor fit has points far from line (large vertical deviations—predictions less reliable). Line captures linear trend, allows prediction (use line to estimate y for new x). For example, in a scatter plot of laps swum vs time, assessing fit by measuring vertical distances from points to the line, judging smaller averages as better. The correct distances to look at are the vertical distances from the points to the line (choice A). A common error is using horizontal distances or distances to the origin, but vertical residuals matter for predicting y from x. Fitting: (1) observe trend direction (upward→positive slope, downward→negative), (2) estimate center of points (where is middle of cloud?), (3) draw line through center following trend (balance points above/below), (4) verify reasonable (does line capture pattern? points fairly close?). Assessing: (1) observe vertical distances from points to line (how far off?), (2) count how many close (within 1-2 grid squares) vs far (5+ squares away), (3) judge: most close=good fit, many far=poor fit, (4) compare alternatives (if multiple lines, which has points closer on average?). Real data: rarely perfect (scatter means variability, line approximates), outliers exist (don't force line to hit outlier—fit majority), linear adequate if points roughly straight trend (even if imperfect). Mistakes: line through outlier ignoring majority, all points above or below (unbalanced), fit by horizontal distance (wrong—vertical distance for y-prediction matters), claiming poor fit is good or vice versa.

Tests informally fitting straight line to scatter plot showing linear association and assessing fit by judging point closeness to line. Linear association (points trending along straight direction) modeled by straight line: fit line informally by drawing through middle of point cloud, balancing points above and below (roughly equal numbers each side). Assess fit: good fit has most points close to line (small vertical distances from points to line—predictions accurate), poor fit has points far from line (large vertical deviations—predictions less reliable). Line captures linear trend, allows prediction (use line to estimate y for new x). For example, in a scatter plot of temperature vs lemonade sales showing upward linear trend, fitting line through approximate center sloping upward, assessing fit by observing most points close to the line vertically (good fit). The correct assessment is yes, a straight line is reasonable because the points show a positive linear association following an upward straight trend (choice A). A common error is thinking a line is only reasonable if it passes through every point or that upward trends require a curve, but lines approximate linear trends even with scatter. Fitting: (1) observe trend direction (upward→positive slope, downward→negative), (2) estimate center of points (where is middle of cloud?), (3) draw line through center following trend (balance points above/below), (4) verify reasonable (does line capture pattern? points fairly close?). Assessing: (1) observe vertical distances from points to line (how far off?), (2) count how many close (within 1-2 grid squares) vs far (5+ squares away), (3) judge: most close=good fit, many far=poor fit, (4) compare alternatives (if multiple lines, which has points closer on average?). Real data: rarely perfect (scatter means variability, line approximates), outliers exist (don't force line to hit outlier—fit majority), linear adequate if points roughly straight trend (even if imperfect). Mistakes: line through outlier ignoring majority, all points above or below (unbalanced), fit by horizontal distance (wrong—vertical distance for y-prediction matters), claiming poor fit is good or vice versa.

Tests informally fitting straight line to scatter plot showing linear association and assessing fit by judging point closeness to line. Linear association (points trending along straight direction) modeled by straight line: fit line informally by drawing through middle of point cloud, balancing points above and below (roughly equal numbers each side). Assess fit: good fit has most points close to line (small vertical distances from points to line—predictions accurate), poor fit has points far from line (large vertical deviations—predictions less reliable). Line captures linear trend, allows prediction (use line to estimate y for new x). For example, in a scatter plot of items bought vs cost showing linear trend, assessing fit as good if 80% of points are within ±1 dollar vertically of the line. The best description is good fit because most points are close to the line with small residuals (choice A). A common error is calling it poor fit because not all points are exactly on the line or suggesting the line should only connect extremes. Fitting: (1) observe trend direction (upward→positive slope, downward→negative), (2) estimate center of points (where is middle of cloud?), (3) draw line through center following trend (balance points above/below), (4) verify reasonable (does line capture pattern? points fairly close?). Assessing: (1) observe vertical distances from points to line (how far off?), (2) count how many close (within 1-2 grid squares) vs far (5+ squares away), (3) judge: most close=good fit, many far=poor fit, (4) compare alternatives (if multiple lines, which has points closer on average?). Real data: rarely perfect (scatter means variability, line approximates), outliers exist (don't force line to hit outlier—fit majority), linear adequate if points roughly straight trend (even if imperfect). Mistakes: line through outlier ignoring majority, all points above or below (unbalanced), fit by horizontal distance (wrong—vertical distance for y-prediction matters), claiming poor fit is good or vice versa.