Correct recorded marks and compare the scatter

Follow all five source steps: STAT → 1:Edit; enter study hours (explanatory $x$) in L1 and test marks (response $y$) in L2; STAT → CALC → 8:LinReg(a+bx); set Xlist=L1 (2nd 1) and Ylist=L2 (2nd 2), then highlight Calculate; press ENTER. The screen gives $r=0.8997013464$, $r^2=0.8094625127$, $a=-6.105276445$, $b=1.982580157$.

In MODE, set STAT DIAGNOSTICS to ON; otherwise $r$ and $r^2$ may be absent from the output even though the regression coefficients are shown. The standalone answer space is blank, but the coefficient is printed in the calculator screen; the 3-s.f. reporting here is authored.

For 8:LinReg(a+bx), $a$ is the intercept and $b$ is the gradient. Thus the full screen equation is $y=-6.105276445+1.982580157x$.

The source also permits 4:LinReg(ax+b). That option labels the gradient $a=1.982580157$ and intercept $b=-6.105276445$. Both options give the same fitted line, $y=1.98x-6.11$ to 3 s.f.; only the coefficient names change. Preserve the equation form rather than copying the letter names without checking.

Replace A’s point $(24,6)$ by $(24,35)$, I’s point $(15,26)$ by $(15,6)$, and E’s point $(52,96)$ by $(52,99)$. Keep all ten students. The source says the new data “removes the outlier point”, meaning that the old A coordinate is replaced, not that student A is deleted. The smallest-hour observation moves down and the largest-hour observation moves up, giving the source’s steeper positive trend.

The diagrams retain every pair and label the corrected observations. An independent numerical check, not required by the printed graphical ask, gives a new slope $2.115879828\ldots$ compared with $1.982580157\ldots$.

The corrected scatter is more tightly clustered around a rising straight-line trend. This is the source’s graphical justification. An independent check gives $r=0.9655543987\ldots$ after correction, compared with $0.8997013464\ldots$ before correction. A steeper slope by itself does not imply a stronger correlation; the scatter’s closeness to a line supplies the separate reason.