10.10 **Educational Content: Understanding Linear Regression through Cricket Chirps and Temperature**---In the study of linear regression, we often explore the relationship between two variables to predict outcomes. Here, we examine the correlation between the number of cricket chirps in one minute and the corresponding temperatures in degrees Fahrenheit (°F). The cricket chirps in one minute serve as the independent variable (x).**Data:**| Chirps in 1 min | 1145 | 862 | 1168 | 978 | 879 | 1027 | 974 | 950 ||-----------------|------|-----|------|-----|-----|------|-----|-----|| Temperature (°F)| 89.1 | 69.5| 84.7 | 78.5| 73.4| 82.2 | 76.4| 81.4|**Task:**1. **Find the Regression Equation:** - Develop a regression equation to model the relationship, using chirps per minute as the independent variable. 2. **Predict Temperature:** - Use the regression equation to predict the temperature when a cricket chirps 3000 times in one minute.3. **Analysis of Prediction:** - Consider why this predicted temperature might not be accurate or realistic.**Graph/Diagram Explanation:**While there is no graph or diagram present, you can visualize this data by plotting the number of chirps on the x-axis and the temperature on the y-axis to form a scatter plot. A best-fit line (regression line) would demonstrate the linear relationship between these variables.**Considerations:**Predicting temperatures based on a much higher number of chirps, such as 3000, may lead to inaccurate predictions due to potential extrapolation well beyond the given data range. Such extrapolation can result in unreliable outcomes because the pattern observed in the provided data may not sustain this far beyond the range. Always ensure predictions with regression remain within reasonable limits defined by the data. The regression equation is given as \( \hat{y} = \_\_ + (\_\_)x \).- Instructions: Round the y-intercept to one decimal place as needed. Round the slope to four decimal places as needed.The task is to determine the best-predicted temperature when a cricket chirps 3000 times in 1 minute, using the regression equation. The predicted temperature, rounded to the nearest integer, should be displayed as \(\_\_\)°F.A question is posed asking what is wrong with this predicted temperature, with multiple choice answers:- A. It is only an approximation. An unrounded value would be considered accurate.- B. The chirps in 1 minute should have been the dependent variable.- C. It is unrealistically high. The value 3000 is far outside of the range of observed values.- D. Nothing is wrong with this value. It can be treated as an accurate prediction.(No graphs or diagrams are present in this text.)

Given that:: Numbers of cricket chirps in minute: Temperature The data set is listed below: 114589.186269.5116884.797878.587973.4102782.297476.495081.4The regression equation is given by:The below table shows the observations and necessary calculations: 114589.186269.57430444830.2559909.0116884.713642247174.0998929.697878.59564846162.2576773.087973.47726415387.5664518.6102782.210547296756.8484419.497476.49486765836.9674413.695081.49025006625.9677330.0Total7983635.2805332350712.72638312.7From the table:, , , , , and The slope parameter is obtained as follows:The intercept parameter is obtained as follows:Therefore, the regression equation is We predicted temperature at a time when a cricket chirps 3000 times in 1 minute, using the regression equation as follows:So, the best-predicted temperature at a time when a cricket chirps 3000 times in 1 minute, based on the regression equation, is .Now, regarding what might be wrong with this predicted temperature, let's analyze the options: It is unrealistically high. The value is far outside the range of observed values.The option is correct.Explanation: It's essential to consider the range of the observed values in your dataset. If is far outside the range of the -values in your dataset, the prediction might not be reliable.Explanation of incorrect options:Option (A) is incorrect because rounding doesn't make the prediction inaccurate, but it's essential to round to an appropriate number of decimal places based on the precision of your data and the context.Option (B) is incorrect because the independent variable (x) is typically the variable being manipulated or controlled, and the dependent variable (y) is what we are trying to predict.Option (D) is incorrect because this would be unlikely. Predictions are subject to the limitations of the model, and the context of the data should be considered.The regression equation is The best-predicted temperature at a time when a cricket chirps 3000 times in 1 minute, based on the regression equation, is .The reason something might be wrong with this prediction is: It is unrealistically high. The value is far outside the range of observed values.The option is correct.

Math

Statistics

Listed below are the numbers of cricket chirps in 1 minute and the corresponding temperatures in °F. Find the regression equation, letting chirps in 1 minute be the independent (x) variable. Find the best predicted temperature at a time when a cricket chirps 3000 times in 1 minute, using the regression equation. What is wrong with this predicted temperature? Chirps in 1 min Temperature (°F) 1145 862 1168 978 879 1027 974 950 89.1 69.5 84.7 78.5 73.4 82.2 76.4 81.4