### Solution Found!

# Late bloomers Japanese cherry trees tend to blossom early

**Chapter , Problem R3.5**

(choose chapter or problem)

**QUESTION:**

Late bloomers? Japanese cherry trees tend to blossom early when spring weather is warm and later when spring weather is cool. Here are some data on the average March temperature (in C) and the day in April when the first cherry blossom appeared over a 24-year period:26 Temperature (C) to first bloom: 4.0 5.4 3.2 2.6 4.2 4.7 4.9 4.0 4.9 3.8 4.0 5.1 Days in April: 14 8 11 19 14 14 14 21 9 14 13 11 Temperature (C) to first bloom: 4.3 1.5 3.7 3.8 4.5 4.1 6.1 6.2 5.1 5.0 4.6 4.0 Days in April: 13 28 17 19 10 17 3 3 11 6 9 11 (a) Make a well-labeled scatterplot thats suitable for predicting when the cherry trees will bloom from the temperature. Describe the direction, form, and strength of the relationship. (b) Use technology to find the equation of the leastsquares regression line. Interpret the slope and y intercept of the line in this setting. (c) The average March temperature this year was 3.5C. When would you predict that the first cherry blossom would appear? Show your method clearly. (d) Find the residual for the year when the average March temperature was 4.5C. Show your work. (e) Use technology to construct a residual plot. Describe what you see. (f) Find and interpret the value of r2 and s in this setting. s Find the slope and y intercept of the least-squares regression line from the means and standard deviations of x and y and their correlation.

### Questions & Answers

**QUESTION:**

Late bloomers? Japanese cherry trees tend to blossom early when spring weather is warm and later when spring weather is cool. Here are some data on the average March temperature (in C) and the day in April when the first cherry blossom appeared over a 24-year period:26 Temperature (C) to first bloom: 4.0 5.4 3.2 2.6 4.2 4.7 4.9 4.0 4.9 3.8 4.0 5.1 Days in April: 14 8 11 19 14 14 14 21 9 14 13 11 Temperature (C) to first bloom: 4.3 1.5 3.7 3.8 4.5 4.1 6.1 6.2 5.1 5.0 4.6 4.0 Days in April: 13 28 17 19 10 17 3 3 11 6 9 11 (a) Make a well-labeled scatterplot thats suitable for predicting when the cherry trees will bloom from the temperature. Describe the direction, form, and strength of the relationship. (b) Use technology to find the equation of the leastsquares regression line. Interpret the slope and y intercept of the line in this setting. (c) The average March temperature this year was 3.5C. When would you predict that the first cherry blossom would appear? Show your method clearly. (d) Find the residual for the year when the average March temperature was 4.5C. Show your work. (e) Use technology to construct a residual plot. Describe what you see. (f) Find and interpret the value of r2 and s in this setting. s Find the slope and y intercept of the least-squares regression line from the means and standard deviations of x and y and their correlation.

**ANSWER:**

a) The scatterplot below shows the relationship between the average March temperature (in C) and the day in April when the first cherry blossom appeared over a 24-year period. The scatterplot shows a positive linear relationship between these two variables. As the average temperature increases, the day in April when the first cherry blossom appears decreases. The form of the relationship is linear with a medium strength.

b) The equation of the least-squares regression line is y = 17.16 - 0.87x. The slope of the line is -0.87, which means that for each degree Celsius increase in the average March temperature, the day in A