Data on the water quality in the eastern United States were obtained by a researcher who wanted to ascertain whether the amount of particulates in water (ppm) could be used to accurately predict the water quality score. Suppose we use the following simple linear regression model:

Quality_i = α+ β× particulates_i + Ɛ_i
Where the deviations Ɛ_i are assumed to be independent and Normally distributed with mean 0 and standard deviation σ. This model was fit to the data using the method of least squares. The following results were obtained from statistical software based on a sample of size 61:
$\begin{array} { | l | c | c | } \hline \text { Variable } & \text { Estimate } & \begin{array} { c } \text { Standard Error of } \\\text { Estimate }\end{array} \\\hline \text { Constant } & 6.214 & 1.003 \\\text { Particulates } & - 0.009 & 0.020 \\\hline\end{array}$ r² = 0.005, s = 0.7896.
Suppose the researcher tests the following hypotheses:
H₀: β₁ = 0, H_a: β₁ 0
What is the value of the t statistic for this test?

Question

Data on the water quality in the eastern United States were obtained by a researcher who wanted to ascertain whether the amount of particulates in water (ppm) could be used to accurately predict the water quality score. Suppose we use the following simple linear regression model:

Quality_i = α+ β× particulates_i + Ɛ_i
Where the deviations Ɛ_i are assumed to be independent and Normally distributed with mean 0 and standard deviation σ. This model was fit to the data using the method of least squares. The following results were obtained from statistical software based on a sample of size 61:

\begin{array} { | l | c | c | } \hline \text { Variable } & \text { Estimate } & \begin{array} { c } \text { Standard Error of } \\\text { Estimate }\end{array} \\\hline \text { Constant } & 6.214 & 1.003 \\\text { Particulates } & - 0.009 & 0.020 \\\hline\end{array}

r² = 0.005, s = 0.7896.
Suppose the researcher tests the following hypotheses:
H₀: β₁ = 0, H_a: β₁ 0
What is the value of the t statistic for this test?

Quizplus · Accepted Answer

The Answer of Data on the water quality in the eastern United States were obtained by a researcher who wanted to ascertain whether the amount of particulates in water (ppm) could be used to accurately predict the water quality score. Suppose we use the following simple linear regression model: Quality_i = α+ β× particulates_i + Ɛ_i Where the deviations Ɛ_i are assumed to be independent and Normally distributed with mean 0 and standard deviation σ. This model was fit to the data using the method of least squares. The following results were obtained from statistical software based on a sample of size 61: $$\begin{array} { | l | c | c | } \hline \text { Variable } & \text { Estimate } & \begin{array} { c } \text { Standard Error of } \ \text { Estimate } \end{array} \ \hline \text { Constant } & 6.214 & 1.003 \ \text { Particulates } & - 0.009 & 0.020 \ \hline \end{array}$$ r² = 0.005, s = 0.7896. Suppose the researcher tests the following hypotheses: H₀: β₁ = 0, H_a: β₁ 0 What is the value of the t statistic for this test?

Data on the Water Quality in the Eastern United States