A manufacturing company wants to study the relationship between advertising investment and sales volume. The following is the Excel output for regression based on market survey data. Please answer the questions based on the output results.某制造公司销售想研究广告投入与销售量之间的关系。下面是根据市场调查数据进行回归的EXcel输出。请根据输出结果回答问题。 SUMMARY OUTPUT输出汇总 Multiple R 0.9307 R Square 0.8662 Adjusted R Square 0.8280 Standard Error 2.0532 Observations 10 ANOVA方差分析 df SS MS Regressive analysis回归分析 1 190.9912 190.9912 Residual残差 8 29.5088 3.6886 Total总计 9 220.5000 斜率Coefficients 标准误差Standard Error Intercep截距 5.0642 2.6306 Advertising investment广告投入 1.8513 0.2814 i）Write a least squares regression equation for predicting sales volume based on advertising investment. 写出以广告投入来预测销售量的最小二乘回归方程 When the advertising investment is 1.9 million yuan, what is the sales volume? 当广告投入为190万元时，销售量为多少万件?

The least squares regression equation for predicting sales volume based on advertising investment is:

Sales Volume = 5.0642 + (1.8513 * Advertising Investment)

When the advertising investment is 1.9 million yuan, the sales volume can be calculated as follows:

Sales Volume = 5.0642 + (1.8513 * 1.9)

Sales Volume = 5.0642 + 3.51847

Sales Volume ≈ 8.58267 million units (rounded to the nearest million units)

相关问题

Use the equation y=5x−2,x∈[0,5]to sample 100 training data. And then train a LinearRegression model and plot the predicted line.

好的，您的第一个问题是使用方程y=5x−2,x∈[0,5]来生成100个训练数据，并训练一个线性回归模型，并绘制预测直线。以下是操作步骤：

首先，我们需要生成100个训练数据。根据给定的方程，我们可以使用Python代码来生成：

import numpy as np

# Generate 100 training data points
X = np.linspace(0, 5, 100)
y = 5 * X - 2

接下来，我们可以使用Scikit-learn的LinearRegression模型来训练模型，并预测新的数据点：

from sklearn.linear_model import LinearRegression

# Train the model on the training data
model = LinearRegression()
model.fit(X.reshape(-1, 1), y.reshape(-1, 1))

# Generate new data points for predictions
X_test = np.linspace(-1, 6, 200)

# Make predictions on the new data points
y_pred = model.predict(X_test.reshape(-1, 1))

最后，我们可以使用Matplotlib库来绘制预测直线：

import matplotlib.pyplot as plt

# Plot the training data and predictions
plt.scatter(X, y)
plt.plot(X_test, y_pred, color='red')
plt.xlabel('x')
plt.ylabel('y')
plt.show()

运行以上代码即可得到预测直线的图像。

需要说明的是，以上代码是使用Python语言实现的。如果您使用的是其他编程语言，操作步骤可能会有所不同，但总体思路是一样的。

Write MATLAB code that implements the parametric bootstrap.Test it using the forearm data.Assume that the normal distribu-tion is a reasonable model for the data.Use your code to get abootstrap estimate of the standard error and the bias of the coeffi-cie

Sure, here is the MATLAB code that implements the parametric bootstrap:

% Load forearm data
load forearm

% Define function that fits linear regression model and returns coefficient estimates
fit_lm = @(x, y) [ones(size(x)), x] \ y;

% Define number of bootstrap samples
B = 1000;

% Define empty arrays to store bootstrap estimates
beta0_boot = zeros(B, 1);
beta1_boot = zeros(B, 1);

% Compute original coefficient estimates
beta_orig = fit_lm(forearm(:, 1), forearm(:, 2));

% Compute standard deviation of residuals
resid_std = std(forearm(:, 2) - beta_orig(1) - beta_orig(2) * forearm(:, 1));

% Perform bootstrap
for i = 1:B
    % Generate bootstrap sample
    y_boot = beta_orig(1) + beta_orig(2) * forearm(:, 1) + randn(size(forearm(:, 1))) * resid_std;
    
    % Fit linear regression model to bootstrap sample
    beta_boot = fit_lm(forearm(:, 1), y_boot);
    
    % Store bootstrap estimates
    beta0_boot(i) = beta_boot(1);
    beta1_boot(i) = beta_boot(2);
end

% Compute bootstrap standard errors and bias
beta0_se = std(beta0_boot);
beta1_se = std(beta1_boot);
beta0_bias = mean(beta0_boot) - beta_orig(1);
beta1_bias = mean(beta1_boot) - beta_orig(2);

% Display results
disp(['Bootstrap standard error of intercept: ', num2str(beta0_se)]);
disp(['Bootstrap standard error of slope: ', num2str(beta1_se)]);
disp(['Bootstrap bias of intercept: ', num2str(beta0_bias)]);
disp(['Bootstrap bias of slope: ', num2str(beta1_bias)]);

This code fits a linear regression model to the forearm data using the `fit_lm` function, which simply calls the backslash operator to perform the least squares optimization. It then defines the number of bootstrap samples `B`, and initializes empty arrays to store the bootstrap estimates.

The code then computes the standard deviation of the residuals of the original model, which is used to generate the bootstrap samples. It then iterates over `B` bootstrap samples, generating a new set of observations by adding Gaussian noise to the original predictions based on the standard deviation of the residuals. It fits a new linear regression model to each bootstrap sample, and stores the resulting coefficient estimates.

Finally, the code computes the standard errors and bias of the bootstrap estimates, and displays the results.