Data were collected over the years from 2001 to 2020 on pumpkin production (in thousands cwt) and average US temperature. Average temperature was then used to predict pumpkin production. O Bivariate Fit of Pumpkin Production By Average US Temperature 18000 16000- 14000 12000 10000 8000 52 52.5 53 53.5 54 54.5 55 55.5 Average US Temperature Summary of Fit Parameter Estimates 0.098305 Term RSquare RSquare Adj Root Mean Square Error Mean of Response Estimate Std Error t Ratio Prob>|t| 0.048211 Intercept -38784.65 35848.62 -1.08 0.2936 2560.642 Average US Temperature 938.25324 669.7694 1.40 0.1783 11427.85 Observations (or Sum Wgts) 20 a Describe the direction, form, and strength of the relationship. Support your description of strength with a numerical value. b) Provide the equation of the regression line. c) Does it make sense to interpret the y-intercept? Explain. d) Predict the pumpkin production for an average temperature of 55 degrees. e) Based on the RSquare value, would you recommend using average temperature to predict pumpkin production? Explain. Pumpkin Production
Data were collected over the years from 2001 to 2020 on pumpkin production (in thousands cwt) and average US temperature. Average temperature was then used to predict pumpkin production. O Bivariate Fit of Pumpkin Production By Average US Temperature 18000 16000- 14000 12000 10000 8000 52 52.5 53 53.5 54 54.5 55 55.5 Average US Temperature Summary of Fit Parameter Estimates 0.098305 Term RSquare RSquare Adj Root Mean Square Error Mean of Response Estimate Std Error t Ratio Prob>|t| 0.048211 Intercept -38784.65 35848.62 -1.08 0.2936 2560.642 Average US Temperature 938.25324 669.7694 1.40 0.1783 11427.85 Observations (or Sum Wgts) 20 a Describe the direction, form, and strength of the relationship. Support your description of strength with a numerical value. b) Provide the equation of the regression line. c) Does it make sense to interpret the y-intercept? Explain. d) Predict the pumpkin production for an average temperature of 55 degrees. e) Based on the RSquare value, would you recommend using average temperature to predict pumpkin production? Explain. Pumpkin Production
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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![**Data Analysis on Pumpkin Production and US Temperature (2001-2020)**
This study explores the relationship between pumpkin production (measured in thousands of cwt) and average US temperature over time. The dataset covers the years 2001 to 2020. A linear regression model was used to predict pumpkin production based on average temperature.
**Graph: Bivariate Fit of Pumpkin Production by Average US Temperature**
- **X-Axis**: Average US Temperature (degrees)
- **Y-Axis**: Pumpkin Production (thousands cwt)
- **Data Points**: Each point represents the production data for a given year.
- **Regression Line**: A line fitting the data suggests the trend of pumpkin production in relation to temperature. The slight positive slope indicates a possible increase in production with higher temperatures.
**Summary of Fit**
- **RSquare**: 0.098305 (indicates the proportion of variance in pumpkin production explained by temperature)
- **RSquare Adj**: 0.048211
- **Root Mean Square Error**: 2506.642 (measures the average distance between the observed and predicted values)
- **Mean of Response**: 11427.85
- **Observations**: 20 data points
**Parameter Estimates**
- **Intercept Estimate**: -38784.65
- **Average US Temperature Estimate**: 938.25324
- **Standard Error, t Ratio, Prob>|t|**: Provided for assessing statistical significance.
**Questions for Analysis**
a) **Describe the direction, form, and strength of the relationship**: The relationship has a positive direction, linear form, but weak strength as indicated by the low RSquare value (0.098305).
b) **Provide the equation of the regression line**:
\[
\text{Pumpkin Production} = 938.25324 \times \text{Temperature} - 38784.65
\]
c) **Interpret the y-intercept**: The y-intercept is -38784.65, which is not interpretable in practical terms as it implies production at zero temperature, an unrealistic condition.
d) **Predict the pumpkin production for an average temperature of 55 degrees**:
\[
\text{Production} = 938.25324 \times 55 - 38784.65 \approx 1288.80 \text{ thousand cwt}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02ac992c-59f5-4674-9c6f-05ab0e575bae%2F36561512-8384-43c5-8d58-2ade02f3ae30%2F8h0n5dc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Data Analysis on Pumpkin Production and US Temperature (2001-2020)**
This study explores the relationship between pumpkin production (measured in thousands of cwt) and average US temperature over time. The dataset covers the years 2001 to 2020. A linear regression model was used to predict pumpkin production based on average temperature.
**Graph: Bivariate Fit of Pumpkin Production by Average US Temperature**
- **X-Axis**: Average US Temperature (degrees)
- **Y-Axis**: Pumpkin Production (thousands cwt)
- **Data Points**: Each point represents the production data for a given year.
- **Regression Line**: A line fitting the data suggests the trend of pumpkin production in relation to temperature. The slight positive slope indicates a possible increase in production with higher temperatures.
**Summary of Fit**
- **RSquare**: 0.098305 (indicates the proportion of variance in pumpkin production explained by temperature)
- **RSquare Adj**: 0.048211
- **Root Mean Square Error**: 2506.642 (measures the average distance between the observed and predicted values)
- **Mean of Response**: 11427.85
- **Observations**: 20 data points
**Parameter Estimates**
- **Intercept Estimate**: -38784.65
- **Average US Temperature Estimate**: 938.25324
- **Standard Error, t Ratio, Prob>|t|**: Provided for assessing statistical significance.
**Questions for Analysis**
a) **Describe the direction, form, and strength of the relationship**: The relationship has a positive direction, linear form, but weak strength as indicated by the low RSquare value (0.098305).
b) **Provide the equation of the regression line**:
\[
\text{Pumpkin Production} = 938.25324 \times \text{Temperature} - 38784.65
\]
c) **Interpret the y-intercept**: The y-intercept is -38784.65, which is not interpretable in practical terms as it implies production at zero temperature, an unrealistic condition.
d) **Predict the pumpkin production for an average temperature of 55 degrees**:
\[
\text{Production} = 938.25324 \times 55 - 38784.65 \approx 1288.80 \text{ thousand cwt}
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