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Recent questions tagged linear-regression

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Go Classes | DA Course | Machine Learning
Suppose you have $m=14$ training examples with $n=3$ features (excluding the additional allones feature for the intercept term, which you should add). The normal equation...
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207
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Go Classes | DA Course | Machine Learning
Kevin is trying to fit a simple linear regression model $\hat{y}=\theta_0+\theta_1 x$ on a dataset with 900 observations.After determining $\hat{\theta_0}$ and $\hat{\the...
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186
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Go Classes | DA Course | Machine Learning
Let's work out a two-way least-squares linear regression method. The $i$ th observation is the ordered pair $\left(x_i, y_i\right)$. We're going to view these data in two...
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167
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Go Classes | DA Course | Machine Learning
The original training loss used for standard least squares regression:$$\operatorname{Loss}(w)=\sum_{i=1}^n\left(y^{(i)}-w^{\top} x^{(i)}\right)^2$$The individual datapoi...
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224
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Go Classes | DA Course | Machine Learning
Let $w^*$ be the solution you obtain in standard least-squares linear regression. What solution do you obtain if you scale all the input features (but not the labels $y$ ...
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185
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Go Classes | DA Course | Machine Learning
Suppose we have a training dataset $D$ for linear regression that is the union of two (disjoint) datasets $A$ and $B$, where $|A| \gg|B|$. For example, $A$ and $B$ might ...
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154
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Go Classes | DA Course | Machine Learning
Using monthly stock averages, $x_1, x_2, \ldots x_n$, you run linear regression without regularization to estimate some future stock value $y$. However, your test error r...
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156
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Go Classes | DA Course | Machine Learning
Consider a modification of the standard linear regression setup where each datapoint is associated with an importance weight. Formally, we have a training dataset consist...
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153
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Go Classes | DA Course | Machine Learning
Consider a modification of the standard linear regression setup where each datapoint is associated with an importance weight. Formally, we have a training dataset consist...
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259
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Go Classes | DA Course | Machine Learning
Consider the following 1-D data set :Beatriz decides that for her application, small errors in the predicted $y$-values are irrelevant. She designs a new loss function $\...
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163
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Go Classes | DA Course | Machine Learning
Consider the following 1-D data set :What is the mean-squared error (MSE) on this data for the hypothesis $ \hat{y}=2x_i $ $?$
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Go Classes | DA Course | Machine Learning
We would like to compare the regression model $\hat{y}=w^2 x+w x $ $(1)$ to the following regression model:$$\hat{y}=w x .... (2)$$Given limited training data, which mod...
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146
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Go Classes | DA Course | Machine Learning
We would like to compare the regression model $\hat{y}=w^2 x+w x $ $(1)$ to the following regression model:$$\hat{y}=w x .... (2)$$Given limited training data, which mod...
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228
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Go Classes | DA Course | Machine Learning
We would like to use the following regression function:$$\hat{y}=w^2 x+w x$$where $x$ is a single value variable. Given a set of training data points $\left\{\left(x_i, y...
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190
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Go Classes | DA Course | Machine Learning
You want to estimate a quantity $y$ as a function of $x$. Suppose you decide to model your estimate $\hat{y}$ as follows:$$\hat{y}=\theta \sqrt{x}$$Note that our model ha...
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207
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Go Classes | DA Course | Machine Learning
Consider a dataset with $N$ examples: $\left\{\left(x_i, y_i\right) \mid 1 \leq i \leq N\right\}$, where both $x_i$ and $y_i$ are real valued for all $i$. The data is mod...
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223
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Go Classes | DA Course | Machine Learning
Consider a dataset with $N$ examples: $\left\{\left(x_i, y_i\right) \mid 1 \leq i \leq N\right\}$, where both $x_i$ and $y_i$ are real valued for all $i$. The data is mod...
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200
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Go Classes | DA Course | Machine Learning
Consider the following data with one input and one output.What is the mean squared training set error of running linear regression on this data (using the model $y=w_0+w_...
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214
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Go Classes | DA Course | Machine Learning
Consider the following data with one input and one output :What is the mean squared leave-one-out cross-validation (LOOCV) error of running linear regression on this data...
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212
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Go Classes | DA Course | Machine Learning
Consider the following data with one input and one output :What is the mean squared test set error of running linear regression on this data, assuming the rightmost three...
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173
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Go Classes | DA Course | Machine Learning
Consider the following data with one input and one output :What is the mean squared training set error of running linear regression on this data (using the model $y=w_0+w...
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151
151 views
Go Classes | DA Course | Machine Learning
Consider the two datasets shown below: D1 and D2. When fitting a linear regression model to predict the $y$-axis value as output, given the $x$ -axis value as input, whic...
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165
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Go Classes | DA Course | Machine Learning
Let's consider regression in one dimension, so our inputs $x^{(i)}$ and outputs $y^{(i)}$ are in $\mathbb{R}$.Linny uses regular linear regression. Given the following da...
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163
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Go Classes | DA Course | Machine Learning
What shape is the objective function when considering both parameters $w$ and $b$ of linear regression $\hat{y}=w x+b$ $?$$$J(w, b)=\frac{1}{2}\left[\left(y^{(1)}-\left(...
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162
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Go Classes | DA Course | Machine Learning
Which is a correct depiction of linear regression error lines for $x \in \mathbb{R}$, $\hat{y}=w x+b$ ABBoth A and BNone of the above
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284
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Go Classes | DA Course | Machine Learning
Consider a scenario where the output has $K$ possible levels ranging from $\{1, \ldots, K\}$. This is typically a classification problem.Can we treat these levels $\{1, \...
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228
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Go Classes | DA Course | Machine Learning
Let $A$ be an $m \times n$ matrix. Which of the following may ba false?  The equation $A^T A \mathbf{x}=A^T \mathbf{b}$ is always consistent for any $\mathbf{b}$ in $\mat...
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180
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Go Classes | DA Course | Machine Learning
Does there exists a $3 \times 2$ matrix $A$ and a vector $b$ such that $A x=b$ does not have a least-squares solution $?$(Please put 0 for False and 1 for True )
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237
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Go Classes | DA Course | Machine Learning
Which of the following is a least square solution $\hat{\mathrm{x}}$ to the equation $$ \left[\begin{array}{cc}1 & -2 \\2 & 1 \\1 & -2 \\2 & 1\end{array}\right] \mathbf{x...
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180
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Go Classes | DA Course | Machine Learning
Let $A=\left[\begin{array}{rr}1 & 3 \\ 1 & 2 \\ 1 & 1\\1 & 2\end{array}\right], \mathbf{b}=\left[\begin{array}{r}5 \\ 2 \\ -2 \\ 3\end{array}\right]$.(A) Write the normal...
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