Question Type 4: Determining the R^2 value for different models on a set of data Exercises

Given the regression sum of squares $SSR=45$ and the residual sum of squares $SSE=15$, calculate the coefficient of determination $R^2$.

A regression yields $SSE=25$ and $SST=125$. Find $R^2$ and describe what it tells you about the model's fit.

If $SSR=40$ and the total sum of squares $SST=50$, find $R^2$.

A model explains 30% of the total variation in $y$. State $R^2$ and compute the ratio $SSE/SST$.

For a dataset one finds $SST=200$ and $SSR=160$. Compute $R^2$ and then find the residual sum of squares $SSE$.

The sample Pearson correlation between $x$ and $y$ is $r=0.8$ and $SST=100$. Assuming a standard linear regression with intercept, find the regression sum of squares $SSR$.

A regression model forced through the origin yields $SSE=20$ and $SST=100$. Calculate $SSR$ and $R^2$ for this model.

A standard linear regression gives a sample correlation $r=0.75$. Compute $R^2$ and explain its interpretation.

Model A on a dataset has $SSR_A=180$ and $SST=250$, while Model B has $SSE_B=10$ and $SST=100$. Compute $R^2$ for both models and state which is better.

In a regression through the origin one can show $SSR= r^2\,SST$. Given that $r=2x$, $SSR=x$, and $SST=10$, find $x$.

Given $\sum(x_i-\bar x)(y_i-\bar y)=80$, $\sum(x_i-\bar x)^2=50$, and $\sum(y_i-\bar y)^2=100$, compute the Pearson correlation $r$ and then $R^2$.