<prompt> Hlalosa tsebetso ea khomphutha ea ho theoha ha likhahla mabapi le ho theoha ha molanan  <response>: Instruction in English: Explain the computational process of gradient descent with respect to linear regression . Response in English: Gradient descent is a popular optimization technique used in machine learning, including linear regression, to find the optimal values of the coefficients that minimize the cost function error.In linear regression, the goal is to find the line of best fit that represents the relationship between the independent and dependent variables. This is done by finding the coefficients weights that minimize the mean squared error MSE, which measures the average squared difference between the predicted and actual values.The gradient descent algorithm follows the negative gradient of the cost function, which represents the direction of the steepest descent, to find the local minimum. It can be thought of as iteratively adjusting the coefficients in a direction that reduces the error.The process of gradient descent in linear regression can be summarized in these steps:1. Initialize the coefficients with random values2. Compute the predicted values using the current coefficients3. Compute the gradient of the cost function with respect to the coefficients4. Update the coefficients by subtracting the computed gradient multiplied by a learning rate5. Repeat steps 2-4 until convergence or until the maximum number of iterations has been reachedDuring each iteration of the gradient descent algorithm, the coefficients are updated using the formula: new_coefficient old_coefficient - learning_rate gradientwhere the learning rate is a hyperparameter that controls the step size of the update. The gradient is computed by taking the partial derivative of the cost function with respect to each coefficient.It is important to choose an appropriate learning rate. If the learning rate is too small, the algorithm may take a long time to converge, but if it is too large, the algorithm may overshoot the minimum and fail to converge.In conclusion, gradient descent is a powerful optimization technique that can be applied to linear regression to find the optimal values of the coefficients that minimize the cost function. By iteratively updating the coefficients, the algorithm adjusts the line of best fit to represent the relationship between the independent and dependent variables. . Response in Sesotho: Ho theoha ha Gradient ke mokhoa o tsebahalang oa ho ntlafatsa o sebelisoang thutong ea mochini, ho kenyeletsoa mokhoa oa ho khutlela morao, ho fumana boleng bo nepahetseng ba li-coefficients tse fokotsang tsebetso ea litšenyehelo phoso. Ka tatellano ea mola, sepheo ke ho fumana moeli o loketseng hantle o emelang kamano lipakeng tsa mefuta e ikemetseng le e itšetlehileng ka eona. Sena se etsoa ka ho fumana li-coefficients litekanyo tse fokotsang phoso ea squared error MSE, e lekanyang phapang e tloaelehileng ea lisekoere pakeng tsa litekanyetso tse boletsoeng esale pele le tsa sebele. Algorithm ea gradient descent e latela gradient e fosahetseng ea tsebetso ea litšenyehelo, e emelang tsela ea ho theoha ho fetisisa, ho fumana bonyane ba sebaka. E ka nkoa e le ho lokisa li-coefficients ka tsela e fokotsang phoso. Tsebetso ea ho theoha ha gradient ka ho fokotseha ha mola e ka akaretsoa ka mehato ena: 1. Qala li-coefficients ka litekanyetso tse sa reroang 2. Bala litekanyetso tse boletsoeng esale pele ka li-coefficients tsa hona joale 3. Bala lebelo la tsebetso ea litšenyehelo mabapi le li-coefficients li-coefficients ka ho tlosa khamera ea khomphutha e atolositsoeng ka sekhahla sa ho ithuta 5. Pheta mehato ea 2-4 ho fihlela ho kopana kapa ho fihlela palo e phahameng ea ho pheta-pheta e fihletsoe Nakong ea ho pheta-pheta ha algorithm ea ho theoha ha likhahla, li-coefficients li nchafatsoa ho sebelisoa foromo: new_coefficient. old_coefficient - learning_rate gradient moo sekhahla sa ho ithuta e leng hyperparameter e laolang boholo ba mohato oa ntlafatso. Gradiente e baloa ka ho nka karolo e nkiloeng ea tšebetso ea litšenyehelo mabapi le coefficient ka ngoe. Ho bohlokoa ho khetha sekhahla se nepahetseng sa ho ithuta. Haeba tekanyo ea ho ithuta e le nyenyane haholo, algorithm e ka na ea nka nako e telele ho kopana, empa haeba e le khōlō haholo, algorithm e ka na ea feta bonyane me ea hlōleha ho kopana. Qetellong, ho theoha ha gradient ke mokhoa o matla oa ho ntlafatsa o ka sebelisoang ho khutlisetsa morao mola ho fumana boleng bo nepahetseng ba li-coefficients tse fokotsang tsebetso ea litšenyehelo. Ka ho ntlafatsa khafetsa li-coefficients, algorithm e lokisa moeli oa ho lekana hantle ho emela kamano lipakeng tsa mefuta e ikemetseng le e itšetlehileng ka eona. 