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Question 1 A Biologist assumes that there is linear relationship between the amount of fertilizer supplied to tomato plants and the subsequent yield of tomatoes obtained. Eight tomato plants, of the same variety were selected at random and treated weekly with a solution in which \( X \) grams of fertilizer was dissolved in a fixed water. The yield y kilograms of tomatoes were recorded. \begin{tabular}{lllllllll} \hline Plant & A & B & C & D & E & F & G & H \\ \hline \( \mathbf{X} \) & 1.0 & 1.5 & 2.0 & 2.5 & 3.0 & 3.5 & 4.0 & 4.5 \\ \hline \( \mathbf{y} \) & 3.9 & 4.4 & 5.8 & 6.6 & 7.0 & 7.1 & 7.3 & 7.7 \\ \hline \end{tabular} a. Calculate Pearson Correlation Coefficient and Interpret the result. b. Conduct the significance test to check the correlation between the variables. Use the significance level 0.05 and 0.01 c. Plot a Scatter Diagram of yield \( Y \) against amount of fertilizer \( X \). d. Calculate Regression line \( Y \) on \( X \) and \( X \) on \( Y \). Predict the value of Yield against Fertilizer. e. Determine the Coefficient of Determination f. Test a Hypothesis for Significance of Coefficient of Determination.

          Question 1
A Biologist assumes that there is linear relationship between the amount of fertilizer supplied to tomato plants and the subsequent yield of tomatoes obtained. Eight tomato plants, of the same variety were selected at random and treated weekly with a solution in which \( X \) grams of fertilizer was dissolved in a fixed water. The yield y kilograms of tomatoes were recorded.
\begin{tabular}{lllllllll}
\hline Plant & A & B & C & D & E & F & G & H \\
\hline \( \mathbf{X} \) & 1.0 & 1.5 & 2.0 & 2.5 & 3.0 & 3.5 & 4.0 & 4.5 \\
\hline \( \mathbf{y} \) & 3.9 & 4.4 & 5.8 & 6.6 & 7.0 & 7.1 & 7.3 & 7.7 \\
\hline
\end{tabular}
a. Calculate Pearson Correlation Coefficient and Interpret the result.
b. Conduct the significance test to check the correlation between the variables. Use the significance level 0.05 and 0.01
c. Plot a Scatter Diagram of yield \( Y \) against amount of fertilizer \( X \).
d. Calculate Regression line \( Y \) on \( X \) and \( X \) on \( Y \). Predict the value of Yield against Fertilizer.
e. Determine the Coefficient of Determination
f. Test a Hypothesis for Significance of Coefficient of Determination.

Question 1
A Biologist assumes that there is linear relationship between the amount of fertilizer supplied to tomato plants and the subsequent yield of tomatoes obtained. Eight tomato plants, of the same variety were selected at random and treated weekly with a solution in which X grams of fertilizer was dissolved in a fixed water. The yield y kilograms of tomatoes were recorded.

Plant A B C D E F G H

𝐗 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

𝐲 3.9 4.4 5.8 6.6 7.0 7.1 7.3 7.7

a. Calculate Pearson Correlation Coefficient and Interpret the result.
b. Conduct the significance test to check the correlation between the variables. Use the significance level 0.05 and 0.01
c. Plot a Scatter Diagram of yield Y against amount of fertilizer X.
d. Calculate Regression line Y on X and X on Y. Predict the value of Yield against Fertilizer.
e. Determine the Coefficient of Determination
f. Test a Hypothesis for Significance of Coefficient of Determination.

Added by Julie A.

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