<prompt> Fumana coefficient of determination r-squared value ea mohlala oa linear regression ka tlase. y 0.5x 0.1x 0, 1, 2, 3, 4, 5 y 0.1, 0.6, 1.1, 1.6, 2.1, 2.6  <response>: Instruction in English: Find the coefficient of determination r-squared value of the linear regression model below.y 0.5x 0.1 . Response in English: The coefficient of determination, also known as the R-squared value, represents the proportion of the variance in the dependent variable y that is predictable from the independent variable x. To calculate the R-squared value, we need to compute the total sum of squares TSS, the regression sum of squares RSS, and the residual sum of squares ESS.First, lets calculate the mean of y:pythonn lenyy_mean sumy nThis gives us a y_mean of 1.41666666666667.Next, we calculate the total sum of squares TSS, which measures the total variance in the dependent variable y: pythonTSS sumyi - y_mean 2 for i in rangenThis gives us a TSS of 5.0666666667.Now we will calculate the predicted y values using the given linear regression equation y 0.5x 0.1:pythony_pred 0.5 xi 0.1 for i in rangenUsing these predicted y values, we can calculate the regression sum of squares RSS, which measures the amount of variance in y that is explained by the independent variable x:python RSS sumy_predi-y_mean 2 for i in rangenThis gives us an RSS of 5.0666666667.Finally, we can calculate the residual sum of squares ESS, which measures the amount of variance in y that is not explained by x:pythonESS sumyi - y_predi 2 for i in rangenSince the data follows the model perfectly, our ESS is 0.Now, we can calculate the coefficient of determination R-squared value using the formula: R2 1 - ESSTSSpython R_squared 1 - ESSTSSIn our example, since the ESS is zero, our R-squared value is 1.0, which indicates that 100 of the variance in y is explained by the independent variable x. It also indicates that the model fits the data perfectly. . Response in Sesotho: Coefficient of determination, eo hape e tsejoang e le R-squared value, e emela karolo ea phapang e itšetlehileng ka y e ka lebelloang ho tloha ho mefuta e ikemetseng x. Ho bala boleng ba R-squared, re hloka ho bala kakaretso ea kakaretso ea lisekoere TSS, palo ea regression ea lisekoere RSS, le kakaretso e setseng ea lisekoere ESS. Taba ea pele, ha re bale moelelo oa y: python n leny y_mean kakaretsoy n Sena se re fa y_mean ea 1.41666666666667. Ka mora moo, re bala kakaretso ea kakaretso ea li-square TSS, e lekanyang kakaretso ea phapang ea mefuta e itšetlehileng ka y: python TSS kakaretso yi - y_mean 2 bakeng sa i ka mefuta e fapaneng. n Sena se re fa TSS ea 5.0666666667. Joale re tla bala litekanyetso tsa y tse boletsoeng esale pele re sebelisa equation ea mela e fanoeng y 0.5x 0.1: python y_pred 0.5 xi 0.1 bakeng sa i in rangen Ho sebelisa tsena tse boletsoeng esale pele. y boleng, re ka bala kakaretso ea kakaretso ea lisekoere RSS, e lekanyang palo ea phapang ho y e hlalosoang ke mofuta o ikemetseng x: python RSS kakaretsoy_predi -y_mean 2 for i in rangen Sena se re fa RSS ea 5.0666666667. Qetellong, re ka bala palo e setseng ea lisekoere ESS, e lekanyang palo ea phapang ho y e sa hlalosoang ke x: python ESS kakaretso yi - y_predi 2 bakeng sa i in rangen Kaha data e latela mohlala ka mokhoa o phethahetseng, ESS ea rona ke 0. Joale, re ka bala coefficient of determination R-squared value re sebelisa foromo: R2 1 - ESSTSS python R_squared 1 - ESSTSS Ka mohlala oa rona, kaha ESS ke lefela, boleng ba rona ba R-squared ke 1.0, e leng se bontšang hore 100 ea phapang ho y e hlalositsoe ke papiso e ikemetseng x. E boetse e bontša hore mohlala o lumellana hantle le data. 