Question Type 5: Connecting pearson's correlation coefficient and determination for linear model with or without parameters Exercises

Given a linear regression model with intercept, the Pearson correlation coefficient satisfies $r = 2x$, the regression sum of squares (SSR) is $x$, and the total sum of squares (SST) is 10. Find the value of $x$.

In a linear model with intercept, you have $r = -3x$, SSR $=2x$, and SST $=18$. Compute $x$ and $R^2$.

For a regression through the origin (no intercept), SSR is 8 and SST (total of squared $y$) is 10. Compute the Pearson correlation coefficient $r$ between $x$ and $y$.

In a linear model with intercept, SST is 20 and the error sum of squares SSE is 12. Calculate $r$, the Pearson correlation coefficient.

A no‐intercept regression yields SSR $=5$ and SSE $=5$. Determine the Pearson correlation coefficient $r$ between $x$ and $y$.

In an intercept model, the Pearson correlation is $r=-0.8$ and SST$=100$. Compute SSR, $R^2$, and SSE.

Suppose in a model with intercept, $r^2=0.64$ and SST$=50$. Find SSR and SSE.

For a regression through the origin, it is stated that $r=2x$, SSR$=x$, and SST$=10$. Solve for $x$.

A no‐intercept regression yields data: $\sum x_i y_i=3$, $\sum x_i^2=2$, and $\sum y_i^2=8$. Calculate SSR, $R^2$, $r$, and SSE.

In a model with intercept, SSR$=30$ and the Pearson correlation is $r=0.5477$. Find SST and SSE.

For a no‐intercept model, the estimated slope is $b=-1.5$, SSR$=45$, and SST$=100$. Find the Pearson correlation coefficient $r$.

In a model with intercept, $r=-0.6$ and error sum of squares SSE$=40$. Compute SST and SSR.