STATISTICS
Refer to the Alpine Botany (Nov. 2012) study of r are plants that grow on the limestone cliffs of the Northern Swiss Jura mountains. Data on altitude above sea level (meters), plant population size (number of plants growing), and molecular variance (i.e., the variance in molecular weight of the plants) for a sample of 12 limestone cliffs are reproduced in the table. Recall that the researchers are interested in whether either altitude or population size is related to molecular variance. $$ \begin{matrix} \text{Cliff Number} & \text{Altitude} & \text{Population Size} & \text{Molecular Variance}\\ \text{1} & \text{468} & \text{147} & \text{59.8}\\ \text{2} & \text{589} & \text{209} & \text{24.4}\\ \text{3} & \text{700} & \text{28} & \text{42.2}\\ \text{4} & \text{664} & \text{177} & \text{59.5}\\ \text{5} & \text{876} & \text{248} & \text{65.8}\\ \text{6} & \text{909} & \text{53} & \text{17.7}\\ \text{7} & \text{1032} & \text{33} & \text{12.5}\\ \text{8} & \text{952} & \text{114} & \text{27.6}\\ \text{9} & \text{832} & \text{217} & \text{35.9}\\ \text{10} & \text{1099} & \text{10} & \text{13.3}\\ \text{11} & \text{982} & \text{8} & \text{3.6}\\ \text{12} & \text{1053} & \text{15} & \text{3.2}\\ \end{matrix} $$ a. Use simple linear regression to investigate the relationship between molecular variance (y) and altitude (x). Find and interpret the value of $r^2$. b. Use simple linear regression to investigate the relationship between molecular variance (y) and population size (x). Find and interpret the value of $r^2$. c. What are your recommendations to the researchers?
STATISTICS
A rare plant that grows on G) the limestone cliffs of the Northern Swiss Jura mountains was studied in Alpine Botany (Nov. 2012). The researchers collected data from a sample of 12 limestone cliffs. Several of the variables measured for each cliff included the altitude above sea level (meters), plant population size (number of plants growing), and molecular variance (i.e., the variance in molecular weight of the plants). These data are provided in the accompanying table. The researchers are interested in whether either altitude or population size is related to molecular variance. $$ \begin{matrix} \text{Cliff} & \text{Altitude} & \text{Population} & \text{Molecular}\\ \text{Number} & \text{ } & \text{Size} & \text{Variance}\\ \text{1} & \text{468} & \text{147} & \text{59.8}\\ \text{2} & \text{589} & \text{209} & \text{24.4}\\ \text{3} & \text{700} & \text{28} & \text{42.2}\\ \text{4} & \text{664} & \text{177} & \text{59.5}\\ \text{5} & \text{876} & \text{248} & \text{65.8}\\ \text{6} & \text{909} & \text{53} & \text{17.7}\\ \text{7} & \text{1032} & \text{33} & \text{12.5}\\ \text{8} & \text{952} & \text{114} & \text{27.6}\\ \text{9} & \text{832} & \text{217} & \text{35.9}\\ \text{10} & \text{1099} & \text{10} & \text{13.3}\\ \text{11} & \text{982} & \text{8} & \text{3.6}\\ \text{12} & \text{1053} & \text{15} & \text{3.2}\\ \end{matrix} $$ a. Use a scatterplot to investigate the relationship between molecular variance and altitude. Do you detect a trend? b. Use a scatterplot to investigate the relationship between molecular variance and population size. Do you detect a trend?