Use the data given below to answer the following question(s).
Following is an extract from the database of a construction company.The table shows the height of walls in feet and the cost of raising them.The estimated simple linear regression equation is given as Ŷ = b0 + b1X.(Hint: Use Excel functions).
$$\begin{array} { | r | r | }
\hline \begin{array} { l }
\text { Height } \
\text { (ft) }
\end{array} & \text { Cost (\$) } \
\hline 4 & 670 \
\hline 3 & 430 \
\hline 7 & 810 \
\hline 9 & 1100 \
\hline 6 & 790 \
\hline 8 & 880 \
\hline 5 & 760 \
\hline 11 & 1200 \
\hline
\end{array}$$
-For a simple linear regression model, significance of regression is:
A)a measure of how well the regression line fits the data.
B)a hypothesis test of whether the regression coefficient ß1 is zero.
C)a statistic that modifies the value of R² by incorporating the sample size and the number of explanatory variables in the model.
D)the variability of the observed Y-values from the predicted values.

Question

Use the data given below to answer the following question(s).
Following is an extract from the database of a construction company.The table shows the height of walls in feet and the cost of raising them.The estimated simple linear regression equation is given as Ŷ = b0 + b1X.(Hint: Use Excel functions).
 $$\begin{array} { | r | r | } 
\hline \begin{array} { l } 
\text { Height } \
\text { (ft) }
\end{array} & \text { Cost (\$) } \
\hline 4 & 670 \
\hline 3 & 430 \
\hline 7 & 810 \
\hline 9 & 1100 \
\hline 6 & 790 \
\hline 8 & 880 \
\hline 5 & 760 \
\hline 11 & 1200 \
\hline
\end{array}$$
-For a simple linear regression model, significance of regression is:
A)a measure of how well the regression line fits the data.
B)a hypothesis test of whether the regression coefficient ß1 is zero.
C)a statistic that modifies the value of R² by incorporating the sample size and the number of explanatory variables in the model.
D)the variability of the observed Y-values from the predicted values.

Quizplus · Accepted Answer

Significance of regression is a hypothesis test of whether the regression coefficient ß1 is zero, i.e. whether there is a significant relationship between the independent variable and the dependent variable. It helps determine if there is evidence of a linear relationship between the two variables. So, option B is the correct choice. Option A is incorrect as it refers to the goodness of fit of the regression line, which is determined by the coefficient of determination (R²). Option C is incorrect as it refers to adjusted R², which is a modified version of R² but does not relate to significance of regression. Option D is incorrect as it refers to residual standard deviation, which is related to the accuracy of the regression model.

Use the Data Given Below to Answer the Following Question(s)